Abstract
In this article, we present exponential finite difference scheme for solving nonlinear two point boundary value problems with Dirichlet's boundary conditions . The local truncation error and under appropriate condition we have discussed the convergence of the proposed method. Numerical experiments demonstrate the use and computational efficiency of the method. Numerical results show that this method is at least fourth order accurate, which is good agreement with the theoretically established order of the method.
Highlights
In the literature, there are many different methods and approaches such as method of integration and discretization which be used to derive the approximate solutions in the domain of these problems [1,2,3,4]
Over the last few decades, high order finite difference method [6,7,8] have generated renewed interest and in recent years, variety of specialized techniques [9,10] for the numerical solution of boundary value problems in ODEs have been reported in the literature
A new method of at least order four is an extension of the method which was developed for the numerical solution of linear problems based on local assumption
Summary
Suppose we wish to determine numerical approximation of the theoretical solution y(x) of the problem y′i yi+1. We note that c and d from equations (7) and (8) respectively, are finite parameters to be determined. We proposed the exponential difference method for solving problem (1) numerically as, yi+1 − 2yi + yi−1 = h2f i exp( h2fi′′ ) , f i = 0, i = 1, 2, ...., N
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