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Vol.1, 2011
A New Third Order Exponentially Fitted Discretization for the Solution of Non-linear Two Point Boundary Value Problems on a Graded Mesh
R. K. Mohanty,Geetan Manchanda,Gunjan Khurana,Arshad Khan
Keywords:Exponentially fitted discretization on a graded mesh; Two point nonlinear boundary value problems; Burger’s Equation; Modified Emden Equation; Vanderpol’s Equation; Hopf bifurcation for the coupled oscillator.
Abstract:
      This paper puts forward a novel graded mesh implicit scheme resting upon full step discretization of order three for computation of non-linear two point boundary value problems. The suggested method is compact and employs three nodal points for the unknown function u(x) in spatial axis. We have also performed error analysis of the cited method. The given method was tried (implemented) upon multiple problems in Cartesian and Polar coordinates with extremely favorable outcomes. This method, though meant for scalar equations, was further extended to compute the vector equations of two point nonlinear boundary value problems. To check the validity of the proposed scheme, we applied it to multiple problems and obtained supporting numerical computations.