Exact Solutions For Systems Of Linear Operator Equations In Reproducing Kernel

Systems of operator equations play very important part in the world of mathe-matics and physics, especially in the field of elastic dynamics, ?uid dynamics, elec-tric dynamics, automatic control. In these fields, many problems belong to systemsof ordinary differential equations of linear coefficient, systems of partial differentialequations of linear coefficient, systems of linear integral equations or systems of linearintegro-differential equations. In order to get the solutions of these systems of equa-tions, mathematicians have made much work. They have given proofs of existenceand uniqueness of solutions of systems of operator equations by using the theorem ofcone and iteration method, the theorem of cone and semi-ordering and the theoremof mixed monotone operator, and fixed point theory, and so on. But, it is importantto get the solutions of systems of operator equations which describe many problemsin the field of natural science and engineering. We usually simplify these systemsof operator equations, then get their approximate solutions. In this paper,their exactsolutions are constructed analytically and are represented in the form of series in thereproducing kernel space. And the n-term approximate to the exact solutions are ob-tained by truncating the series. Systems of integro-differential equations are studiedto demonstrate the accuracy of the present method,and results obtained by the methodis simple and effective.