[HTML][HTML] Haar wavelet collocation method for three-dimensional elliptic partial differential equations

I Aziz, M Asif - Computers & Mathematics with Applications, 2017 - Elsevier
A new collocation method based on Haar wavelet is presented for numerical solution of
three-dimensional elliptic partial differential equations with Dirichlet boundary conditions. An …

A cubic B-spline semi-analytical algorithm for simulation of 3D steady-state convection-diffusion-reaction problems

J Lin, S Reutskiy - Applied Mathematics and Computation, 2020 - Elsevier
In this work, a new cubic B-spline-based semi-analytical algorithm is presented for solving
3D anisotropic convection-diffusion-reaction (CDR) problems in the inhomogeneous …

[HTML][HTML] A fourth-order arithmetic average compact finite-difference method for nonlinear singular elliptic PDEs on a 3D smooth quasi-variable grid network

N Jha, B Singh - MethodsX, 2023 - Elsevier
The analysis of nonlinear elliptic PDEs representing stationary convection-dominated
diffusion equation, Sine-Gordon equation, Helmholtz equation, and heat exchange diffusion …

[HTML][HTML] A new high order compact off-step discretization for the system of 3D quasi-linear elliptic partial differential equations

RK Mohanty, N Setia - Applied Mathematical Modelling, 2013 - Elsevier
We present a new fourth order compact finite difference scheme based on off-step
discretization for the solution of the system of 3D quasi-linear elliptic partial differential …

[HTML][HTML] A RBF-based technique for 3D convection–diffusion–reaction problems in an anisotropic inhomogeneous medium

S Reutskiy, J Lin - Computers & Mathematics with Applications, 2020 - Elsevier
We present a RBF-based semi-analytical technique for solving 3D convection–diffusion–
reaction (CDR) equations to model transport in an anisotropic inhomogeneous medium. The …

Compact higher order discretization of 3D generalized convection diffusion equation with variable coefficients in nonuniform grids

D Deka, S Sen - Applied Mathematics and Computation, 2022 - Elsevier
A higher-order compact (HOC) discretization of generalized 3D convection-diffusion
equation (CDE) in nonuniform grid is presented. Even in the presence of cross-derivative …

Preconditioned techniques for solving large sparse linear systems arising from the discretization of the elliptic partial differential equations

SM Molavi-Arabshahi, M Dehghan - Applied mathematics and computation, 2007 - Elsevier
In this paper, we use the BiCG, BiCGSTAB methods as preconditioned techniques. Also we
compare the preconditioned Krylov subspace methods such as GMRES, GMRES (m), QMR …

Maximum norm error analysis of a nonmatching grids finite element method for linear elliptic PDEs

M Boulbrachene, Q Al Farei - Applied Mathematics and Computation, 2014 - Elsevier
In this paper, we study a nonmatching grid finite element approximation of linear elliptic
PDEs in the context of the Schwarz alternating domain decomposition. We show that the …

Exponential basis and exponential expanding grids third (fourth)-order compact schemes for nonlinear three-dimensional convection-diffusion-reaction equation

N Jha, B Singh - Advances in Difference Equations, 2019 - Springer
This paper addresses exponential basis and compact formulation for solving three-
dimensional convection-diffusion-reaction equations that exhibit an accuracy of order three …

A novel B-spline method to analyze convection-diffusion-reaction problems in anisotropic inhomogeneous medium

S Reutskiy, Y Zhang, J Lin, J Lu, H Xu, Y He - Engineering Analysis with …, 2020 - Elsevier
We present a B-spline based semi-analytical technique for solving 2D convection-diffusion-
reaction equations. The main feature of the presented technique is to separate the …