scholarly journals Numerical Solution and Simulation of Second-Order Parabolic PDEs with Sinc-Galerkin Method Using Maple

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Aydin Secer
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Numerical Solution ◽  
Equation System ◽  
Solution Algorithm ◽  
Basis Functions ◽  
Algebraic Equations ◽  
Parabolic Pdes ◽  
Linear Partial Differential Equations ◽  
Type Boundary

An efficient solution algorithm for sinc-Galerkin method has been presented for obtaining numerical solution of PDEs with Dirichlet-type boundary conditions by using Maple Computer Algebra System. The method is based on Whittaker cardinal function and uses approximating basis functions and their appropriate derivatives. In this work, PDEs have been converted to algebraic equation systems with new accurate explicit approximations of inner products without the need to calculate any numeric integrals. The solution of this system of algebraic equations has been reduced to the solution of a matrix equation system via Maple. The accuracy of the solutions has been compared with the exact solutions of the test problem. Computational results indicate that the technique presented in this study is valid for linear partial differential equations with various types of boundary conditions.

scholarly journals Computational Sinc-scheme for extracting analytical solution for the model Kuramoto-Sivashinsky equation

2019 ◽  
Vol 9 (5) ◽  
pp. 3720
Author(s):  
Kamel Al-Khaled ◽  
Issam Abu-Irwaq
Keyword(s):  
Analytical Solution ◽  
Galerkin Method ◽  
Numerical Solution ◽  
Present Article ◽  
Point Theory ◽  
Algebraic Equations ◽  
Time Direction ◽  
Numerical Examples ◽  
Sivashinsky Equation ◽  
Crank Nicolson

The present article is designed to supply two different numerical<br />solutions for solving  Kuramoto-Sivashinsky equation. We have made<br />an attempt to develop a numerical solution via the use of<br />Sinc-Galerkin method for  Kuramoto-Sivashinsky equation, Sinc<br />approximations to both derivatives and indefinite integrals reduce<br />the solution to an explicit system of algebraic equations. The fixed<br />point theory is used to prove the convergence of the proposed<br />methods. For comparison purposes, a combination of a Crank-Nicolson<br />formula in the time direction, with the Sinc-collocation in the<br />space direction is presented, where the derivatives in the space<br />variable are replaced by the necessary matrices to produce a system<br />of algebraic equations. In addition, we present numerical examples<br />and comparisons to support the validity of these proposed<br />methods.

An Integral Formulation Approach for Numerical Solution of Tubular Reactors Models

2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Eliseo Hernandez-Martinez ◽  
Jose Alvarez-Ramirez ◽  
Francisco J. Valdes-Parada ◽  
Hector Puebla
Keyword(s):  
Boundary Conditions ◽  
Numerical Solution ◽  
Tubular Reactor ◽  
Reaction Diffusion ◽  
Integral Formulation ◽  
Tubular Reactors ◽  
Type Boundary ◽  
Reactor Models ◽  
Diffusion Convection ◽  
Direct Incorporation

In this paper, we derive an integral formulation approach based on Green’s function for the numerical solution of tubular reactor models described by reaction-diffusion-convection (RDC) equations with Danckwerts-type boundary conditions. The integral formulation approach allows the direct incorporation of boundary conditions and leads to a stable and accurate numerical integration with smooth round-off error. Numerical simulations of two of tubular reactors models are presented in order to illustrate the numerical accuracy of the method. The results are compared with those resulting from using standard finite difference method. Our results show that the integral formulation approach improves the performance of classical FD schemes.

scholarly journals Numerical solution of linear stochastic Volterra integral equations via new basis functions

Filomat ◽  
2019 ◽  
Vol 33 (18) ◽  
pp. 5959-5966
Author(s):  
Tofigh Cheraghi ◽  
Morteza Khodabin ◽  
Reza Ezzati
Keyword(s):  
Linear System ◽  
Numerical Solution ◽  
Integral Equations ◽  
Orthogonal Basis ◽  
Volterra Integral Equations ◽  
Basis Functions ◽  
New Method ◽  
Algebraic Equations ◽  
Numerical Examples

In this article, we use a new method based on orthogonal basis functions for the numerical solution of stochastic Volterra integral equations of the second kind (SVIE). By using this method, a SVIE can be reduced to a linear system of algebraic equations. Finally, to show the efficiency of the proposed method, we give two numerical examples.

scholarly journals A Hybrid Differential Transforms and Finite Difference Method to Numerical Solution of Convection–Diffusion Equation

2021 ◽  
Vol 8 (6) ◽  
pp. 90-94
Author(s):  
Noorulhaq Ahmadi ◽  
Mohammadi Khan Mohammadi
Keyword(s):  
Partial Differential Equations ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Diffusion Equation ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Difference Method ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Type Boundary

In this work, we discuss a hybrid-based method on differential transforms and a finite difference method to numerical solution of convection–diffusion equation with Dirichlet’s type boundary conditions. The developed method is tested on various problems and the numerical results are reported in tabular and figure form. This method can be easily extended to handle non-linear convection–diffusion partial differential equations.

Sign in / Sign up

Export Citation Format

Share Document