Abstract
In this article, we presented a non-uniform mesh size high order exponential finite difference scheme for the numerical solutions of two point boundary value problems with Dirichlet's boundary conditions. Under appropriate conditions, we have discussed the local truncation error and the convergence of the proposed method. Numerical experiments have been carried out to demonstrate the use and high order computational efficiency of the present method in several model problems. Numerical results showed that the proposed method is accurate and convergent. The order of accuracy is at least cubic which is in good agreement with the theoretically established order of the method.
Highlights
Over the last few decades, finite difference methods [6,7,8] have generated renewed interest and in recent years, variety of specialized techniques [10,11] for the numerical solution of boundary value problems in ODEs have been reported in the literature
The purpose of this article is to propose an exponential finite difference method with variable step size for problem (1). The development of this numerical method for two-point boundary-value problems plays a paramount role in the approximate solution of boundary value problems with a small parameter affecting the highest derivative of the differential equation
It is a well known fact that singularly perturbed boundary value problem possess a small interval in which the solution varies rapidly and this small interval is known as the boundary layer in the literature
Summary
Over the last few decades, finite difference methods [6,7,8] have generated renewed interest and in recent years, variety of specialized techniques [10,11] for the numerical solution of boundary value problems in ODEs have been reported in the literature. An exponential finite difference method with uniform step size was proposed in [12] for the numerical solution of linear two point boundary value problem. The purpose of this article is to propose an exponential finite difference method with variable step size for problem (1).
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