Quintic B-spline collocation method for fourth order partial integro-differential equations with a weakly singular kernel

摘要

Quintic B-spline collocation method for the numerical solution of fourth order partial integro-differential equations is considered. The scheme is based on the second order backward differential formula in the time direction and the quintic B-spline method for the spatial derivative. Some numerical experiments are included to demonstrate the effectiveness of the discrete technique. From the numerical experiments, we can find that the present scheme possesses high accuracy and efficiency, and the numerical results are in good agreement with the exact solutions.