LEGENDRE WAVELETS METHOD FOR SOLVING THE DERIVATIVE DEPENDENT DOUBLY SINGULAR BOUNDARY VALUE PROBLEMS

. Different class of derivative dependent doubly singular boundary value problems exist in different areas of science and engineering like a heat distribution in a steady state, fluid dynamics, mechanical engineering, aerospace engineering and medical science etc. It is a familiar fact that the solutions of boundary value problems have singular nature near the corners and edges of the domain. The singularities are of type's vertex, edge, vertex-edge singularities. Due to presence of singularities the classical numerical methods are unable to yield accurate numerical solutions and rate of convergence of these methods degrades. This is due to the fact that, in particularly finite element method discretized equations results ill-conditioned matrices which leads to small change in the system or forcing function will make large difference in the solution. In order to reduce the condition number, improve effectiveness of computations and exactness of the solutions; it is desirable to find efficient methods along with standard numerical methods such as finite difference method, FEM, multigrid, wavelet multigrid methods and so on. In this paper, we have developed the Legendre wavelet technique for the numerical solution of derivative-dependent doubly singular boundary value problems. The proposed technique is developed with the Legendre wavelets and the results shows the better exactness of the proposed Legendre wavelets method, their results can be clarified through the numerical test problems.