The Galerkin method for the numerical solution of some class of differential equations by utilizing Gegenbauer wavelets
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Abstract
Many differential equations that emerge from modeling physical phenomena do not always possess well-known analytical solutions. Additionally, wavelets have attracted considerable attention from both theoretical and applied researchers in recent decades. In this study, we introduce the Galerkin method for numerically solving a specific class of differential equations by employing Gegenbauer wavelets (GWGM). In this approach, Gegenbauer wavelets serve as weight functions and are treated as basis elements, enabling us to derive the numerical solution. The numerical solutions obtained through this method are compared with several existing methods and the exact solution. Various examples are presented to demonstrate the effectiveness and applicability of the proposed technique.
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