Generalized Solutions Of Boundary Value Problems With Jump Discontinuity (submitted In Partial Fulfillment Of The M. Sc. Degree In Mathematics)

We study on how to find a generalized solution of boundary value problems of different orders with jump discontinuity. Here first, second order linear inhomogeneous differential equations are considered and then we extend it to the nth order. Green’srnfunction plays a great role for solving such differential equations.rnClassical theory is based on solving first- or higher-order derivatives with jumps on both sides of the boundaries and then attempting to satisfy the boundary conditions. Our aim is to develop the vector analysis of functions with jump discontinuities across surfaces and boundaries that cannot be solved by classical techniques. With the help of this we can solve many unsolved problems in the potential, scattering and wave propagation theories. Furthermore, problems whose solutions are already known can be solved by this method in a very simple fashion.rnWe can also show that there is a new solution of linear homogeneous systems of differential equations with singular in coefficients, in the space of generalized functions other than the classical solutions

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