Abstract
In this paper, fourth order stable central difference method is presented for solving self-adjoint singular perturbation problems for small values of perturbation parameter, e . First, the given differential equation was reduced to its conventional form and then it was transformed into linear system of algebraic equations in the form of a three-term recurrence relation, which can easily be solved by using Thomas Algorithm. To validate the applicability of the method, four model examples have been solved for different values of perturbation parameter and mesh sizes. The numerical results are tabulated and compared with some of the previous findings reported in the literature and it is observed that the present method is more efficient. Graphs are also depicted in support of the numerical results. Both theoretical error bounds and numerical rate of convergence have been established for the method. Key Words/Phrases: Singular perturbation; stable central difference method; self-adjoint.
Highlights
Any differential equation obtained from a given differential equation and having the property that its solution is an integrating factor of the other is known as adjoint differential equation
This gives a large algebraic system of equations to be solved by any iterative methods in place of the differential equation to give the solution at the grid points and the solution is obtained at grid points
We present fourth order stable central difference method that is accurate and easy for solving self-adjoint singularly perturbed two-point boundary value problems for small values of perturbation parameter ε
Summary
Any differential equation obtained from a given differential equation and having the property that its solution is an integrating factor of the other is known as adjoint differential equation. (Saini and Mishra , 2015) presented an algorithm to develop approximate solution of third-order self-adjoint singularly perturbed two-point boundary value problem in which the highest order derivative is multiplied by a small parameter.
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