Numerical Treatment of First Order Volterra Integro-Differential Equation Using Non-Polynomial Spline Functions.

The approach given in this paper leads to numerical methods to find the approximate solution of volterra integro -diff. equ.1st kind. First, we reduce it from integro VIDEs to integral VIEs of the 2nd kind by using the reducing theory, then we use two types of Non-polynomial spline function (linear, and quadratic). Finally, programs for each method are written in MATLAB language and a comparison between these two types of Non-polynomial spline function is made depending on the least square errors and running time. Some test examples and the exact solution are also given. [ABSTRACT FROM AUTHOR]