volterra integro- differential equations in a hilbert space

volterra integro- differential equations in a hilbert space

in the hilbert space Ꚛⁿ _j=1 (w⁴₂ [a,b] Ꚛ w⁴₂ [a,b]). based on the concept of the reproducing kernel function combined with gram-schmidt orthogonalization process, we represent an exact solution in a form of fourier series in the reproducing kernel hilbert space Ꚛⁿ _j=1 (w²₂ [a,b] Ꚛ w²₂ [a,b]). accordingly, the approximate solution of the system of fuzzy volterra integro-differential equations is obtained by the n-term intercept of the exact solution and proved to converge to the exact solution. finally, two numerical examples are presented to illustrate the reliability, appropriateness and efficiency of the method.