Difference kernel iterative method for linear and nonlinear partial differential equations. Issue 3 (April 2016)

• Record Type: Journal Article
• Authors: Khan, Yasir; Faraz, Naeem; Smarda, Zdenek
• Is Part Of: Neural computing & applications. Volume 27:Issue 3(2016)
• Page Start: 671
• Page End: 675
• Publication Date: 2016-04
• Subjects: Difference kernel -- Laplace transformation -- Convolution theorem; Neural networks (Computer science) -- Periodicals; Neural circuitry -- Periodicals; Artificial intelligence -- Periodicals; Neural Networks (Computer) -- Periodicals; Réseaux neuronaux (Informatique) -- Périodiques; Réseaux nerveux -- Périodiques; Intelligence artificielle -- Périodiques; 006.32
• DOI: 10.1007/s00521-015-1886-z
• Languages: English
• ISSNs: 0941-0643

Abstract

Abstract The purpose of this paper was to propose a new method to solve partial differential equations arising in the field of science and engineering. In this new method, we have reduced the multiple integrals into a single integral and expressed it in terms of a difference kernel. To make the calculation easy and convenient, we have used the Laplace transformation to solve the difference kernel. The method is very simple, easy to understand and calculation minimizing as compared to the Adomian decomposition method and the variational iteration method. Some examples are given to verify the reliability and efficiency of the method.