An Efficient Computational Method for Handling Singular Second-Order, Three Points Volterra Integrodifferential Equations
In this paper, a powerful computational algorithm is developed for the solution of classes of singular second-order, three-point Volterra integrodifferential equations in favorable reproducing kernel Hilbert spaces. The solutions is represented in the form of series in the Hilbert space
W
2
3[0, 1] with easily computable components. In finding the computational solutions, we use generating the orthogonal basis from the obtained kernel functions such that the orthonormal basis is constructing in order to formulate and utilize the solutions. Numerical
experiments are carried where two smooth reproducing kernel functions are used throughout the evolution of the algorithm to obtain the required nodal values of the unknown variables. Error estimates are proven that it converge to zero in the sense of the space norm. Several computational simulation
experiments are given to show the good performance of the proposed procedure. Finally, the utilized results show that the present algorithm and simulated annealing provide a good scheduling methodology to multipoint singular boundary value problems restricted by Volterra operator.
Keywords: Integrodifferential Equation of Volterra Type; Multipoint Boundary Conditions; Reproducing Kernel Method; Singular Boundary Value Problem
Document Type: Research Article
Affiliations: 1: Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan 2: Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt 19117, Jordan 3: Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, Jordan 4: Nonlinear Analysis and Applied Mathematics Research Group, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Publication date: 01 November 2016
- Journal of Computational and Theoretical Nanoscience is an international peer-reviewed journal with a wide-ranging coverage, consolidates research activities in all aspects of computational and theoretical nanoscience into a single reference source. This journal offers scientists and engineers peer-reviewed research papers in all aspects of computational and theoretical nanoscience and nanotechnology in chemistry, physics, materials science, engineering and biology to publish original full papers and timely state-of-the-art reviews and short communications encompassing the fundamental and applied research.
- Editorial Board
- Information for Authors
- Submit a Paper
- Subscribe to this Title
- Terms & Conditions
- Ingenta Connect is not responsible for the content or availability of external websites
- Access Key
- Free content
- Partial Free content
- New content
- Open access content
- Partial Open access content
- Subscribed content
- Partial Subscribed content
- Free trial content