Non-local Solution of Mixed Integral Equation with Singular Kernel (Global Journal of Science Frontier Research, 2015)
In this paper, we consider a non-local mixed integral equation in position and time in the space 2 L 1,1 C 0,T ;T. Then, using a quadratic numerical method, we have a system of Fredholm integral equations (SFIEs), where the existence of a unique solution is considered. Moreover, we consider Product Nystrom method (PNM), as a famous method to solve the singular integral equations, to obtain an algebraic system. Finally, some numerical results are considered, and the error estimate, in each case, is computed.
Keywords: non-local solution; fredholm-volterra integral equation; system of fredholm integral equations; weakly kernel; algebraic system