Indirect RBF for High-Order Integro-Differential Equations

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.