Numerical solution of high-order linear VIDEs by using Taylor collocation method

What is it about?

The main purpose of this work is to provide a new direct numerical method for high-order linear Volterra integro-differential equations (VIDEs). An algorithm based on the use of Taylor polynomials is developed for the numerical solution of high-order linear VIDEs. It is shown that this algorithm is convergent. Numerical results are presented to prove the effectiveness of the presented algorithm.

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Why is it important?

This method is easy to implement and one of the advantages of this method is that not only the high order of convergence, but also the present method is direct and the approximate solution is given by using explicit formulas and there is no algebraic system needed to be solved, which makes the proposed algorithm very effective and easy to implement.

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