Indirect RBF for High-Order Integro-Differential Equations
Jafar Biazar *
Department of Applied Mathematics, Faculty of Mathematical Science, University of Guilan, P.O. Box 41635-19141, P.C. 41938-33697, Rasht, Iran.
Mohammad Ali Asadi
Department of Applied Mathematics, Faculty of Mathematical Science, University of Guilan, P.O. Box 41635-19141, P.C. 41938-33697, Rasht, Iran.
*Author to whom correspondence should be addressed.
Abstract
Two di erent approaches are applied to solve high-order integro-di erential equations (IDEs), based on Radial Basis Functions (RBF). The rst approach, which is called the direct approach (DRBF) is based on di erentiation, and considers the solution as a nite linear combination of RBFs. While the second, the indirect approach (IRBF), is based on integration and considers the highest order derivative of the solution as a nite linear combination of RBFs. The results of this study indicate that for low-order IDEs, both approaches are enough accurate, but for high-order IDEs, the IRBF solutions are more accurate than those of direct RBF. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.
Keywords: High order integro-di erential equations (IDEs), Direct Radial Basis Functions (DRBF), Indirect Radial Basis Functions (IRBF), Legendre-Gauss-Lobatto quadrature, Iterated integrals.