New Algorithms to Solve Integral Equations Automatically

Integral equations come from a wide range of applications. Laplace transform has been playing an important role in mathematics; it is very powerful and widely used in solving integral equations, however, such a traditional method suffers a serious drawback, which is the calculation of inverse Laplace transform. Such a kind of inverse calculation is problematic or impossible, except some very simple functions. Sumudu transform is a new integral transform with nice features like Laplace transform, in addition, it provides new methodology for problem solving. In this work, a new computational method is proposed to solve integral equations, the new method incorporates useful features from both Laplace transform and Sumudu transform such that the calculation of the inverse Laplace transform is avoided. In addition, it is demonstrated with implementations that the new method and techniques presented in this work can be implemented in computer algebra systems such as Maple to solve Volterra convolution integral equations and mixed differential Volterra convolution integral equations automatically