A REFINED GALERKIN APPROACH FOR SOLVING HIGHER-ORDER DIFFERENTIAL EQUATIONS VIA BERNOULLI POLYNOMIALS

This paper introduces a novel Galerkin algorithm, employing Bernoulli polynomials, to efficiently solve high-order differential equations and systems with homogeneous and nonhomogeneous initial conditions. The algorithm’s efficacy hinges on the strategic selection of trial functions that align with the problem’s initial conditions. Illustrative examples validate the proposed algorithm’s validity and efficiency. Comparative analyses against existing spectral methods emphasize the superior performance of the new algorithm.

• Galerkin method
• Bernoulli polynomials
• higher-order differential equations
• systems of differential equations
• trial functions
• spectral methods
• numerical solution of ODEs

• Mathematical functions and polynomials
• Numerical methods for differential equations
• Fractional Differential Equations Solutions
• Galerkin method
• Bernoulli polynomials
• higher-order differential equations
• systems of differential equations
• trial functions
• spectral methods
• numerical solution of ODEs
• Applied Mathematics
• Numerical Analysis
• Modeling and Simulation
• Mathematics