A finite-element approach, based on cubic B-spline collocation, is presented for the numerical solution of Troeschâ€™s problem. The method is used on both a uniform mesh and a piecewise-uniformâ€¦ (More)

Certain pairs of Runge-Kutta methods may be used additively to solve a system of n differential equations x' = J(t)x + g(t, x). Pairs of methods, of order p < 4, where one method is semiexplicit andâ€¦ (More)

Consider a system of differential equations x = f(x). Most methods for the numerical solution of such a system may be characterized by a pair of matrices (A, B) and make no special use of anyâ€¦ (More)

The aim of this article is to introduce a novel Laplace variational numerical scheme, based on the variational iterationmethod (VIM) and Laplace transform, for the solution of certain classes ofâ€¦ (More)

Three different spline-based approaches for solving Bratu and Bratu-type equations are presented. The classical cubic spline collocation method, an adaptive spline collocation on nonuniformâ€¦ (More)