# Registered Data

Contents

- 1 [CT102]
- 1.1 [00032] A geometrically preservative semi-adaptive method for the numerical solution of Kawarada equations
- 1.2 [00314] The Orthogonal Spline Collocation Method for Parabolic Problems with Interfaces
- 1.3 [00328] Schrödinger map and Multifractality
- 1.4 [00104] High order approximation of Caputo-Prabhakar derivative and its application in solving time fractional Advection-Diffusion equation
- 1.5 [00111] A convergent numerical method for time-fractional reaction-diffusion equation
- 1.6 [00513] The perfectly matched layer for elastic waves in layered media
- 1.7 [00999] High-order energy stable schemes for the phase-field model by the Convex Splitting Runge-Kutta methods
- 1.8 [01005] Nonlinear Disturbance Observer-Based Control Design for Markovian Jump Systems
- 1.9 [01012] Uncertainty and disturbance estimator design for interval type-2 fuzzy systems
- 1.10 [01014] Fault detection asynchronous filter design for Markovian jump fuzzy systems under cyber attacks
- 1.11 [01848] A Higher Order Schwarz Domain Decomposition Method for Singularly Perturbed Differential Equation
- 1.12 [01248] Reduction of Computational Cost with Optimal Accurate Approximation for Boundary Layer Originated Two Dimensional Coupled System of Convection Diffusion Reaction Problems
- 1.13 [02229] Efficient numerical methods for time-fractional Black-Scholes equation arising in finance
- 1.14 [01742] A signed distance function preserving scheme for mean curvature flow and related applications
- 1.15 [01634] Mimetic schemes applied to the convection diffusion equation: A numerical comparison.
- 1.16 [01142] Thermodynamically Consistent Finite Volume Schemes for Electrolyte Simulations
- 1.17 [01004] An Error Estimate for an Implicit-Upwind Finite Volume Scheme for Boussinesq Model
- 1.18 [02560] A Composite Adaptive Finite Point Method for 2D Burgers' Equation
- 1.19 [02452] Fifth-order WENO Schemes with Z-type Nonlinear Weights for Hyperbolic Conservation Laws
- 1.20 [01015] VMSFE Analysis of Transient MHD-NS Flow

# [CT102]

**Session Time & Room**- CT102 (1/4) :
__1E__@__E702__[Chair: Qin Sheng] - CT102 (2/4) :
__2C__@__E702__[Chair: Siyang Wang] - CT102 (3/4) :
__2D__@__E702__[Chair: AAKANSHA AAKANSHA] - CT102 (4/4) :
__2E__@__E702__[Chair: Jürgen Fuhrmann] **Classification**- CT102 (1/4) : Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (
__65M__) - CT102 (2/4) : Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (
__65M__) / Stability of control systems (__93D__) - CT102 (3/4) : Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (
__65M__) - CT102 (4/4) : Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (
__65M__) / Numerical methods for ordinary differential equations (__65L__)

## [00032] A geometrically preservative semi-adaptive method for the numerical solution of Kawarada equations

**Session Time & Room**:__1E__(Aug.21, 17:40-19:20) @__E702__**Type**: Contributed Talk**Abstract**: This presentation concerns the numerical stability and geometric preservations of the numerical solution of Kawarada equation problems. The nonlinear partial differential equations exhibit strong quenching types of singularities that represent a number of key characteristics from industrial and multi-physical applications. A second order semi-adaptive implicit finite difference method will be constructed and investigated. We shall begin with a detailed mathematical analysis of the stability without freezing singular source terms of Kawarada equations in this talk. Preservation features of the solution vector sequences will then be studied. Realistic orders of the convergence will be given via generalized Milne's devices. Finally, computer simulations will be carried out to demonstrate the effectiveness of the theoretical analysis and conclusions.**Classification**:__65M06__,__65M12__,__65M50__,__68U01__,__65D18__**Format**: Talk at Waseda University**Author(s)**:**Qin Sheng**(Baylor University)

## [00314] The Orthogonal Spline Collocation Method for Parabolic Problems with Interfaces

**Session Time & Room**:__1E__(Aug.21, 17:40-19:20) @__E702__**Type**: Contributed Talk**Abstract**: The parabolic problems with interfaces are solved using a method in which orthogonal spline collocation (OSC) is employed for the spatial discretization and the Crank–Nicolson method for the time-stepping. The derivation of the method is described in detail for the case in which cubic monomial basis functions are used in the development of the OSC discretization. The results of extensive numerical experiments involving examples from the literature are presented.**Classification**:__65M06__,__65M22__,__65M55__,__65M70__,__35K05__**Format**: Talk at Waseda University**Author(s)**:**Danumjaya Palla**(BITS-Pilani KK Birla Goa Campus)- Santosh Kumar Bhal (Centurion University of Technology and Management)
- Graeme Fairweather (Mathematical Reviews, American Mathematical Society)

## [00328] Schrödinger map and Multifractality

**Session Time & Room**:__1E__(Aug.21, 17:40-19:20) @__E702__**Type**: Contributed Talk**Abstract**: In this talk, we will explore the richness of the Schrödinger map equation by discussing some recent results on its evolution in both hyperbolic and Euclidean geometrical settings. In the latter case, the equivalent form of the equation describes the motion of a vortex filament, e.g., smoke rings, tornadoes, etc. With numerical, theoretical techniques, we will show that when the filament curve initially has corners, its evolution and the trajectory of its corners exhibit multifractality.**Classification**:__65M06__,__28A80__,__11L05__,__65M20__,__35Q55__,__Mathematical physics, Numerical methods, Schrödinger-type equtaions, Hyperbolic space__**Format**: Talk at Waseda University**Author(s)**:**Sandeep Kumar**(CUNEF University)- Luis Vega (Basque Center for Applied Mathematics)
- Francisco de la Hoz (The University of the Basque Country)

## [00104] High order approximation of Caputo-Prabhakar derivative and its application in solving time fractional Advection-Diffusion equation

**Session Time & Room**:__1E__(Aug.21, 17:40-19:20) @__E702__**Type**: Contributed Talk**Abstract**: This work aims to devise a high-order numerical scheme to approximate the CaputoPrabhakar derivative of order 0 < α < 1, using an rth degree Lagrange interpolation polynomial, where $3\leq r\in\mathbb{Z^{+}}.$. This numerical scheme can be thought of as an extension of the presented schemes for the approximation of the Caputo-Prabhakar derivative in our previous work \cite{r1}. Further, we adopt the proposed scheme to solve a time-fractional Advection-Diffusion equation with the Dirichlet boundary condition. It is shown that the method is unconditionally stable, uniquely solvable, and convergent with convergence order, $ O(\tau^{r+1-\alpha}, h^{2}), $ where τ and h are the step sizes in the temporal and spatial directions, respectively. Without loss of generality, obtained results are supported by numerical examples for r = 4, 5. \bibitem{r1} Deeksha Singh, Farheen Sultana, and Rajesh K Pandey, Approximation of Caputo Prabhakar derivative with application in solving time fractional advection-diffusion equation, International Journal for Numerical Methods in Fluids. $94(7)(2022)$, pp. 896-919.**Classification**:__65M06__,__65M12__,__Numerical approximation of fractional derivative and its application__**Format**: Talk at Waseda University**Author(s)**:**DEEKSHA SINGH**(Department of Mathematical Sciences, Indian Institute of Technology, BHU, Varanasi)- Rajesh K. Pandey (Department of Mathematical Sciences, Indian Institute of Technology, BHU, Varanasi)

## [00111] A convergent numerical method for time-fractional reaction-diffusion equation

**Session Time & Room**:__1E__(Aug.21, 17:40-19:20) @__E702__**Type**: Contributed Talk**Abstract**: This paper design and analyze a robust finite difference scheme for solving a time-fractional reaction-diffusion equation with smooth and non-smooth solutions. The solution of this equation exhibits a weak singularity at the initial time $\mathrm{t}=0$. So we use graded temporal mesh in order to handle the singularity. We discretize the space variable using a cubic polynomial spline difference scheme. Further, the stability and convergence for both the smooth and non-smooth solutions are analyzed separately.**Classification**:__65M06__,__65M12__**Format**: Online Talk on Zoom**Author(s)**:**Anshima Singh**(Indian Institute of Technology (BHU) Varanasi)

## [00513] The perfectly matched layer for elastic waves in layered media

**Session Time & Room**:__2C__(Aug.22, 13:20-15:00) @__E702__**Type**: Contributed Talk**Abstract**: The perfectly matched layer (PML) is widely used to truncate domains in large-scale simulation of wave propagation in open boundaries. PML absorbs outgoing waves without reflection and significantly improves computational efficiency. However, it is very challenging to prove stability of PML models. In this talk, I present our recent contribution on the stability analysis of PML models for the elastic wave equation in layered media modeling seismic wave propagation in the Earth layers.**Classification**:__65M06__,__65M12__,__86-08__**Format**: Talk at Waseda University**Author(s)**:**Siyang Wang**(Umeå University)

## [00999] High-order energy stable schemes for the phase-field model by the Convex Splitting Runge-Kutta methods

**Session Time & Room**:__2C__(Aug.22, 13:20-15:00) @__E702__**Type**: Contributed Talk**Abstract**: The Convex Splitting Runge-Kutta method is a high-order energy stable scheme for gradient flow which is a combination of the well-known convex splitting method and the multi-stage Runge-Kutta method. In this talk, we will discuss the applications and challenges of CSRK via extensive examples of the phase-field model.**Classification**:__65M06__,__65M12__,__65M70__,__Phase-field model, Convex splitting method, Runge-Kutta method__**Format**: Talk at Waseda University**Author(s)**:**Jaemin Shin**(Chungbuk National University)- Hyun Geun Lee (Kwangwoon University)
- June-Yub Lee (Ewha Womans University)

## [01005] Nonlinear Disturbance Observer-Based Control Design for Markovian Jump Systems

**Session Time & Room**:__2C__(Aug.22, 13:20-15:00) @__E702__**Type**: Contributed Talk**Abstract**: This paper addresses the anti-disturbance control problem for time-delayed Markovian jump nonlinear systems with modeled and unmodeled disturbances. Specifically, the modeled disturbance is generated by a nonlinear exogenous system and estimated using a nonlinear disturbance observer. A mode-dependent asymmetric Lyapunov-Krasovskii functional is used to derive sufficient conditions for the existence of the proposed controller and disturbance observer. A numerical example is included to demonstrate the efficacy of the theoretical results developed.**Classification**:__93D05__,__93D15__,__93E15__,__LYAPUNOV STABILITY; SYSTEMS AND CONTROL THEORY__**Format**: Online Talk on Zoom**Author(s)**:**KAVIARASAN BOOMIPALAGAN**(CHUNGBUK NATIONAL UNIVERSITY)- OH-MIN KWON (CHUNGBUK NATIONAL UNIVERSITY)

## [01012] Uncertainty and disturbance estimator design for interval type-2 fuzzy systems

**Session Time & Room**:__2C__(Aug.22, 13:20-15:00) @__E702__**Type**: Contributed Talk**Abstract**: This article investigates the uncertainty and disturbance estimator-based control problem for the interval type-2 fuzzy systems. By designing the appropriate filter, the proposed control designs can estimate system uncertainties and external disturbances accurately. By using the Lyapunov-Krasovskii stability theorem, the required stability conditions and the control gain matrices for the system under consideration are obtained. Finally, an illustrative example is demonstrated to verify the feasibility of the proposed control method.**Classification**:__93D05__,__93D09__,__93D15__,__Lyapunov Stability, Systems and Control Theory, Fuzzy Systems__**Format**: Online Talk on Zoom**Author(s)**:**KAVIKUMAR RAMASAMY**(CHUNGBUK NATIONAL UNIVERSITY)- KWON OH-MIN (CHUNGBUK NATIONAL UNIVERSITY)

## [01014] Fault detection asynchronous filter design for Markovian jump fuzzy systems under cyber attacks

**Session Time & Room**:__2C__(Aug.22, 13:20-15:00) @__E702__**Type**: Contributed Talk**Abstract**: This work is concerned with the issue of fault detection asynchronous filter design for a class of discrete-time Markovian jump fuzzy systems with cyber attacks. Precisely, the cyber attacks phenomenon in the network environment satisfies the Bernoulli distribution. Finally, the applicability and usefulness of the proposed filter design method is verified through a practical example.**Classification**:__93D05__,__93D09__,__93D20__,__Lyapunov Stability of control systems__**Format**: Online Talk on Zoom**Author(s)**:**Sakthivel Ramalingam**(Chungbuk National University)- Oh-Min Kwon (Chungbuk National University)

## [01848] A Higher Order Schwarz Domain Decomposition Method for Singularly Perturbed Differential Equation

**Session Time & Room**:__2D__(Aug.22, 15:30-17:10) @__E702__**Type**: Contributed Talk**Abstract**: We consider a fourth order singularly perturbed differential equation. To solve the problem, the differential equation is transformed into a coupled system of singularly perturbed differential equations. The original domain is divided into three overlapping subdomains. On the regular subdomain, a hybrid scheme is used, while a compact fourth order difference scheme is used on the two boundary layer subdomains on a uniform mesh. We demonstrate that proposed scheme is nearly fourth order uniformly convergent.**Classification**:__65M06__**Format**: Online Talk on Zoom**Author(s)**:**AAKANSHA AAKANSHA**(Indian Institutes of Technology (Banaras Hindu University) Varanasi)

## [01248] Reduction of Computational Cost with Optimal Accurate Approximation for Boundary Layer Originated Two Dimensional Coupled System of Convection Diffusion Reaction Problems

**Session Time & Room**:__2D__(Aug.22, 15:30-17:10) @__E702__**Type**: Contributed Talk**Abstract**: In this talk, I will consider a generalized form of a coupled system of time dependent convection diffusion reaction problems having arbitrary small diffusion terms, which lead to boundary layers. The numerical approximations of these problems require adaptive mesh generation for uniformly convergent approximation. In the present talk, I will provide an algorithm which will reduce the computational cost of the system solver by converting the system of discrete equations to a tridiagonal matrix form. This approach together with an adaptive mesh generation technique will preserve the optimal convergence accuracy. This convergence is proved to be independent of diffusion terms magnitude.**Classification**:__65M06__,__65M50__,__65N50__,__Computational Cost Reduction, Error Analysis, Adaptive Mesh Generation, Coupled System of Time Dependent PDEs, Two Dimension__**Format**: Online Talk on Zoom**Author(s)**:**Pratibhamoy Das**(Indian Institute of Technology Patna)- Pratibhamoy Das (Indian Institute of Technology Patna)
- Shridhar Kumar (Indian Institute of Technology Patna)

## [02229] Efficient numerical methods for time-fractional Black-Scholes equation arising in finance

**Session Time & Room**:__2D__(Aug.22, 15:30-17:10) @__E702__**Type**: Contributed Talk**Abstract**: Two numerical schemes to solve time-fractional Black-Scholes PDE governing European options. are proposed. First, fractional derivative is discretized by L1-scheme and spatial derivatives by cubic spline method on uniform mesh. Secondly, we discretize temporal variable by L1-scheme on non-uniform mesh and spatial derivatives by NIPG method on uniform mesh. Stability, convergence and numerical results are carried out. Three European options are priced as application and impact of time-fractional derivative order on option price is shown.**Classification**:__65M06__,__65M12__,__65M15__**Format**: Online Talk on Zoom**Author(s)**:**Jaspreet Kaur Anand**(Indian Institute of Technology Guwahati, Guwahati, Assam)- Natesan Srinivasan (Indian Institute of Technology Guwahati, Guwahati, Assam)

**Session Time & Room**:__2D__(Aug.22, 15:30-17:10) @__E702__**Type**: Contributed Talk**Abstract**: Mean curvature flow is an important research topic in geometry, applied mathematics, and the natural sciences. In this talk, we propose a scheme for solving mean curvature flow and some related problems efficiently and accurately on Cartesian grids. Our method uses the sign distance function defined in a narrowband near the moving interface to represent the evolution of the curve. We derive the equivalent evolution equations of distance function in the narrowband. The novelty of the work is to determine the equivalent evolution equation on Cartesian girds without extra conditions or constraints. The proposed method extends the differential operators appropriately so that the solutions on the narrowband are the distance function of the solution to the original mean flow solution. Furthermore, the extended solution carries the correct geometric information, such as distance and curvature, on Cartesian grids. Consequently, it is possible to adapt the existing numerical methods, for instance, finite difference or WENO scheme, that are developed on the Cartesian grids to solve PDEs on curves. The computational domain is a thin narrowband whose widths are a small constant multiple of uniform Cartesian grid spacing. Some experiments confirm that the proposed method is convergent numerically.**Classification**:__65M06__**Author(s)**:**Chia-Chieh Jay Chu**(National Tsing Hua UniversityB)

## [01634] Mimetic schemes applied to the convection diffusion equation: A numerical comparison.

**Session Time & Room**:__2D__(Aug.22, 15:30-17:10) @__E702__**Type**: Contributed Talk**Abstract**: Mimetic Finite Difference Schemes (DFM) are increasingly present in the numerical resolution of transient problems [1] since they are more precise than traditional Finite Difference (DF) schemes. However, there are methods in DF that use appropriate combinations of schemes in different nodes in order to eliminate the numerical spread of the method, [2]. In these cases, DF methods are more accurate than DFM. In this work, we start from the equation of convection-diffusion of an incompressible fluid ∂u/∂t+v·∇u=∇·(K∇u), (1) where u(x, t) represents the unknown of the problem, v(x, t) is the velocity, K is the diffusion tensor, and DFM is defined that eliminates the numerical diffusion presented by traditional DFM schemes. To measure the effectiveness of the mimetic schemes, for different configurations of (1), they are compared with the equivalent schemes in DF with the same order of precision as the DFM; for this purpose, the second-order schemes proposed by [2, 3] are taken. Finally, different comparisons are made to verify the results obtained by the given schemes. References: [1] Castillo J. and Grone R.D. A matrix analysis approach to higher-order approximations for divergence and gradients satisfying a global conservation law. SIAM J. Matrix Anal. Appl., 25(1):128– 142, 2003. [2] Mehdi Dehghan. Weighted finite difference techniques for the one-dimensional advection-diffusion equation. Applied Mathematics and Computation, 147(2):307–319, 2004. [3] Mehdi Dehghan. Quasi-implicit and two-level explicit finite-difference procedures for solving the one-dimensional advection equation. Applied Mathematics and Computation, 167(1):46–67, 2005.**Classification**:__65M06__,__65M99__**Author(s)**:**Jorge Ospino**(Universidad del Norte)- Giovanni Calderon (Universidad Industrial de Santander)
- Jorge Villamizar (Universidad Industrial de Santander)

## [01142] Thermodynamically Consistent Finite Volume Schemes for Electrolyte Simulations

**Session Time & Room**:__2E__(Aug.22, 17:40-19:20) @__E702__**Type**: Contributed Talk**Abstract**: In order to account for finite ion sizes and solvation effects, the classical Nernst-Planck-Poisson system describing ion transport in electrolytes needs to be enhanced by cross-diffusion - like terms. For this situation, we present a space discretization scheme which adapts the classical Scharfetter-Gummel exponential fitting upwind flux for the Voronoi box finite volume method. Numerical examples use the Julia package VoronoiFVM.jl which takes advantage of automatic differentiation to handle the strong nonlinearities of the system.**Classification**:__65M08__,__65M12__,__78A57__,__65N08__,__35Q81__**Format**: Talk at Waseda University**Author(s)**:**Jürgen Fuhrmann**(Weierstrass Institute for Applied Analysis and Stochastics)- Benoit Gaudeul (Univ. Paris Saclay)

## [01004] An Error Estimate for an Implicit-Upwind Finite Volume Scheme for Boussinesq Model

**Session Time & Room**:__2E__(Aug.22, 17:40-19:20) @__E702__**Type**: Contributed Talk**Abstract**: This study contains an error estimate for a Finite Volume Method-based Implicit-Upwind scheme for the d-dimensional(d=2 or 3) Boussinesq Model, which describes several buoyancy-driven Hydrodynamic phenomena such as natural-convection in a cavity and Marsigli Flow. For each time level, the L2- norms of the error for the temperature and velocity components are found to be of order (h + k), where h is the spatial grid size and k is the time step size.**Classification**:__65M08__,__65M15__,__65N08__,__65N15__**Format**: Talk at Waseda University**Author(s)**:**Chitranjan Pandey**(Indian Institute of Technology Kanpur, India)- B.V. Rathish Kumar (Indian Institute of Technology Kanpur, India)

## [02560] A Composite Adaptive Finite Point Method for 2D Burgers' Equation

**Session Time & Room**:__2E__(Aug.22, 17:40-19:20) @__E702__**Type**: Contributed Talk**Abstract**: This paper focuses on solving the unsteady 2D Burgers equation. We present a minimal machinery algorithm based on an operator splitting technique into different temporal levels in conjunction with an adaptive finite point method (AFPM). The advisability of the AFPM is that it efficiently adjusts itself to fit into the local properties of the exact solution, and its user-friendliness makes it easy to implement and cost-effective. Mathematical estimates like stability, consistency, and convergence analysis support the presented method.**Classification**:__65M06__,__65M12__**Author(s)**:**Ashish Awasthi**(National Institute of Technology Calicut)- Sreelakshmi A (National Institute of Technology Calicut)
- Shyaman V P (National Institute of Technology Calicut)

## [02452] Fifth-order WENO Schemes with Z-type Nonlinear Weights for Hyperbolic Conservation Laws

**Session Time & Room**:__2E__(Aug.22, 17:40-19:20) @__E702__**Type**: Contributed Talk**Abstract**: In this talk, we propose the variant Z-type nonlinear weights in the fifth-order weighted essentially non-oscillatory (WENO) finite difference scheme for hyperbolic conservation laws. We take new smoothness indicators and follow the form of Z-type nonlinear weights introduced by Borges et al., leading to fifth order accuracy in smooth regions and sharper approximations around discontinuities. Finally, numerical examples are presented to demonstrate the advantages of the proposed WENO schemes in shock-capturing.**Classification**:__65M06__**Author(s)**:**Jiaxi Gu**(Pohang University of Science and Technology)- Xinjuan Chen (Jimei University)
- Jae-Hun Jung (Pohang University of Science and Technology)

## [01015] VMSFE Analysis of Transient MHD-NS Flow

**Session Time & Room**:__2E__(Aug.22, 17:40-19:20) @__E702__**Type**: Contributed Talk**Abstract**: In this work, a thorough investigation of the transient magnetohydrodynamic Navier-Stokes (MHD-NS) equations is carried out applying variational multiscale stabilized finite element (VMSFE) technique. The convergence characteristics of VMSFE scheme (Apriori Estimate) has been derived in this study. The VMSFE method's credibility is stablished by numerical experiments on multiply driven cavity flow. The flow pattern is traced for various Hartmann, Reynolds, and magnetic force inclination angle values.**Classification**:__65L60__,__65K15__**Format**: Talk at Waseda University**Author(s)**:**Anil Rathi**(Indian Institute of Technology, Kanpur (India))- B.V. Rathish Kumar (Indian Institute of Technology, Kanpur (India))
- Dipak Kumar Sahoo (Indian Institute of Technology, Kanpur)