Three point discretization of order four and six for (du :dx) of the solution of non-linear singular two point boundary value problem

We present finite difference methods of order four and six for the numerical solution of (du/dx) for the non-linear differential equation u″ = f(x,u,u′), 0 < x > 1 subject to the boundary conditions u(0) = A, u(l) =B. The proposed methods require only three grid points and applicable to both s...

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Bibliographic Details
Published inInternational journal of computer mathematics Vol. 78; no. 1; pp. 123 - 139
Main Authors Mohanty, R. K., Evans, D. J., Shivani Dey
Format Journal Article
LanguageEnglish
Published Abingdon Gordon and Breach Science Publishers 01.01.2001
Taylor and Francis
Subjects
Burger's equation
Exact sciences and technology
Finite difference methods
First order derivative
G.1.7
Local truncation error
Mathematical analysis
Mathematics
Non-linear equation
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Ordinary differential equations
RMS errors
Sciences and techniques of general use
Singular equation
Central difference scheme
Differential equation
Singular equation
Numerical method
Boundary condition
Burgers equation
Truncation error
Non linear equation
Boundary value problem
Numerical solution
First order
Derivative
Comparative study
Finite difference method
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Summary:We present finite difference methods of order four and six for the numerical solution of (du/dx) for the non-linear differential equation u″ = f(x,u,u′), 0 < x > 1 subject to the boundary conditions u(0) = A, u(l) =B. The proposed methods require only three grid points and applicable to both singular and non-singular problems. Numerical examples are given to illustrate the methods and their convergence.
ISSN:0020-7160
1029-0265
DOI:10.1080/00207160108805101