B-splines methods with redefined basis functions for solving fourth order parabolic partial differential equations

摘要

In this work, we discuss two methods for solving a fourth order parabolic partial differential equation. In Method-I, we decompose the given equation into a system of second order equations and solve them by using cubic B-spline method with redefined basis functions. In Method-II, the equation is solved directly by applying quintic B-spline method with redefined basis functions. Stability of these methods have been discussed. Both methods are unconditionally stable. These methods are tested on four examples. The computed results are compared wherever possible with those already available in literature. We have developed Method-I for fourth order non homogeneous parabolic partial differential equation from which we can obtain displacement and bending moment both simultaneously, while Method-II gives only displacement. The results show that the derived methods are easily implemented and approximate the exact solution very well.