Volterra Integral Equations Using Non Polynomial Spline Functions

This book attempts to study and modify some numerical methods to solve two types of linear Volterra integral equations of the second kind which are: Linear Volterra integral equations (VIE's) . Linear Volterra integral equations with weakly Singular kernel. Two different kinds of non-polynomial spline functions including (Linear and Quadratic) have been applied for the first time to treat the above problem. Also, Linear Volterra integral equations of the first kind are reduced to VIE's of the second kind and therefore we treat them numerically in the same way. Moreover, fourteen examples are presented to demonstrate the applicability, accuracy and efficiency of the method on one hand and to confirm the convergence order on the other hand. Also, convergence analysis of the method is discussed. Finally, at the end of each method we give algorithms and programs are developed and written in MATLAB\ R12, 2012.