Abstract
We present a new numerical algorithm for two-point boundary value problems. We first present the exact solution in the form of series and then prove that then-term numerical solution converges uniformly to the exact solution. Furthermore, we establish the numerical stability and error analysis. The numerical results show the effectiveness of the proposed algorithm.
Highlights
It is well known that many problems can be presented by the following two-point boundary value problems:[xαy (x)] = f (x, y), x ∈ (0, 1), (1)y (0) = a, y (1) = b, where α ∈ [0, 1], a, and b are finite constants
We prove that the n-term numerical solution yn(x) converges uniformly to the exact solution
We use the reproducing kernel iterative method to solve a class of two-point boundary value problems
Summary
It is well known that many problems can be presented by the following two-point boundary value problems:. Problem (1) arises from many fields of applied mathematics and physics, such as nuclear physics, economical system, chemical engineering, and underground water flow. Aziz and Kumar [1, 2] presented a finite difference method based on nonuniform mesh to solve this problem. We propose a new numerical algorithm to solve (1) by using the reproducing kernel theory.
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