ABSTRACT
Due to the wide existence and applicability of ordinary and partial differential equations in various branches of science and engineering, a variety of nonlinear systems of initial and boundary value problems have been extensively studied in the literature. In the collocation method, the numerical solution of a differential equation is obtained as a linear combination of basis functions with unknown coefficients to be determined. The theory of B-spline function is well known in obtaining the approximate numerical solution of boundary value problems, either ordinary or partial differential equations due to their distinct properties. B-spline basis functions are also in trigonometric and exponential forms. In the collocation method, using B-spline approximation leads to a technique that requires only the unknown parameters at certain node points to generate the solution. The B-spline basis functions are widely used to solve various linear and nonlinear ordinary and partial differential equations.
