Numerical Solutions of a Class of Second Order Boundary Value Problems on Using Bernoulli Polynomials
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Abstract
The aim of this paper is to find the numerical solutions of the second order linear and nonlinear differential equations with <i>Dirichlet</i>, <i>Neumann</i> and <i>Robin</i> boundary conditions. We use the Bernoulli polynomials as linear combination to the approximate solutions of 2nd order boundary value problems. Here the Bernoulli polynomials over the interval [0,1] are chosen as trial functions so that care has been taken to satisfy the corresponding homogeneous form of the <i>Dirichlet</i> boundary conditions in the Galerkin weighted residual method. In addition to that the given differential equation over arbitrary finite domain [<i>a,b</i>] and the boundary conditions are converted into its equivalent form over the interval [0,1]. All the formulas are verified by considering numerical examples. The approximate solutions are compared with the exact solutions, and also with the solutions of the existing methods. A reliable good accuracy is obtained in all cases.
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