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Efficient Numerical Scheme for Generalized Black–Scholes Equations on Piecewise Uniform Shishkin-Type Mesh
In this paper, we propose numerical techniques for solving generalized Black–Scholes partial differential equations. The proposed numerical method is...
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Efficient Method for Solving the Boltzmann Equation on a Uniform Mesh
AbstractA new numerical method for solving the Boltzmann equation on a uniform mesh in velocity space is proposed. The asymptotic complexity of the...
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Fitted Difference Scheme on a Non-uniform Mesh for Singularly Perturbed Parabolic Reaction–Diffusion with Large Negative Shift and Non-local Boundary Condition
In this paper, we study the numerical solution of singularly perturbed parabolic reaction–diffusion problems with large delay in space, and the right...
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A non-uniform Haar wavelet method for a singularly perturbed convection–diffusion type problem with integral boundary condition on an exponentially graded mesh
In this article, we present a numerical approach based on non-uniform Haar wavelets on an exponentially graded mesh to approximate the solution of a...
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Richardson extrapolation method for 2D-SPP on VB mesh singularly perturbed convection–diffusion problem on a Vulanović–Bakhvalov mesh
This paper discusses the Richardson extrapolation technique of an upwind finite difference scheme on a modified Bakhvalov-type mesh (named...
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Towards a Volume Mesh Generator Tailored for NEFEM
The conversion of digital models from computer-aided design (CAD) to meshes for computer-aided engineering (CAE) is a well-known bottleneck, because...
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Coupe: A Mesh Partitioning Platform
This paper presents Coupe, a mesh partitioning platform. It provides solutions to solve different variants of the mesh partitioning problem, mainly...
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Stability and Error Analysis of an Efficient Numerical Method for Convection Dominated Parabolic PDEs with Jump Discontinuity in Source Function on Modified Layer-Adapted Mesh
AbstractThis paper introduces a novel approach for analyzing efficient numerical solution of a class of singularly perturbed parabolic...
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GAUSSIAN-RBF INTERPOLANT AND THIRD-ORDER COMPACT DISCRETIZATION OF 2D ANOMALOUS DIFFUSION-CONVECTION MODEL ON A MESH-MAPPED NON-UNIFORM GRID NETWORK
We describe a compact finite-difference discretization and Gaussian-radial basis function for the two-dimensional local fractional elliptic PDEs that...
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The supercloseness of the finite element method for a singularly perturbed convection-diffusion problem on a Bakhvalov-type mesh in 2D
For singularly perturbed convection-diffusion problems, supercloseness analysis of the finite element method is still open on Bakhvalov-type meshes,...
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Space-time CutFEM on overlap** meshes I: simple continuous mesh motion
We present a cut finite element method for the heat equation on two overlap** meshes: a stationary background mesh and an overlap** mesh that...
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Analysis of Numerical Differential Formulas on a Bakhvalov Mesh in the Presence of a Boundary Layer
AbstractThe paper considers numerical differentiation of functions with large gradients in the region of an exponential boundary layer. This topic is...
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Space-time CutFEM on overlap** meshes II: simple discontinuous mesh evolution
We present a cut finite element method for the heat equation on two overlap** meshes: a stationary background mesh and an overlap** mesh that...
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A fast uniformly accurate global numerical approximation to solution and scaled derivative of system of singularly perturbed problems with multiple diffusion parameters on generalized adaptive mesh
The aim of this article is to analyze a robust numerical approximation to the solution along with the scaled first derivative (physically known as diff...
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Optimally Convergent Isoparametric \(P^2\) Mesh Generation
This paper describes a framework for the generation of \(P^2\)...
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Numerical solution of a time dependent singularly perturbed delay differential equation on an exponentially graded mesh
In this article, we consider a singularly perturbed time-dependent reaction-diffusion problem with a large delay in space direction. The problem...
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Uniform convergence analysis of a new adaptive upwind finite difference method for singularly perturbed convection-reaction-diffusion boundary value problems
In this paper, a new adaptive upwind finite difference method based on the arc-length equidistribution principle is studied for solving the general...
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A Uniform and Pressure-Robust Enriched Galerkin Method for the Brinkman Equations
This paper presents a pressure-robust enriched Galerkin (EG) method for the Brinkman equations with minimal degrees of freedom based on EG velocity...
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A Stable Time-Dependent Mesh Method for Generalized Credit Rating Migration Problem
The r-adaptive difference scheme is advanced in this article for solving the generalized credit rating migration model for arbitrary volatility with...
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An almost second order parameter uniform scheme for 2D singularly perturbed boundary turning point problem
In this article, we propose to construct and analyze a higher order parameter uniform numerical scheme for a class of two dimensional (2D) parabolic...
