Simplified iterative reproducing kernel method for handling time-fractional BVPs with error estimation

By M. Al‐Smadi. Ain Shams Engineering Journal, 2017

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Abstract In this article, we introduce a novel numerical scheme, the iterative reproducing kernel method (IRKM), for providing numerical approximate solutions of a certain class of time-fractional boundary value problem within favorable aspects of the reproducing kernel Hilbert space in Caputo sense. The algorithm methodology is based on generating an orthonormal basis from the reproducing kernel function to formulate the solution in form of uniformly convergent series, accordance with the constraint conditions in the space ω 5 [ 0 , 1 ] . Error estimates in the ω 5 -norm are obtained as well as numerical experiments are described to represent the hypothesis, and to confirm the design procedure of the proposed algorithm. The numerical results indicate that the IRKA is a significant development tool for handling such issues arising in computer, physics and engineering fields.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/0f93f26345d39a32a78df5770c97cbcf56d435a5