Volterra Integro- Differential Equations in a Hilbert Space

In the Hilbert Space (???????) . Based on the concept of the reproducing kernelfunction combined with Gram-schmidt orthogonalization process, we represent an exact solutionin a form of fourier series in the reproducing kernel Hilbert space (????????)Accordingly, the approximate solution of the system of fuzzy Volterra integro-differentialequations is obtained by the n-term intercept of the exact solution and proved to converge to theexact solution. Finally, two numerical examples are presented to illustrate the reliability,appropriateness and efficiency of the method.

Keywords:

Hilbert space , Voltera differential equation , integral equation