Finite Element Solution And Laser Transmission Of The Initial Value Problem Of Second Order Differential Equations With Singular Coefficients Solitary Wave Initial State Numerical Simulation,

In this paper, we discuss about the finite element solutions of the 2-order ordinary differential problems with singular coefficients and based on the discussion we study the numerical simulation of the initial state for the laser transmission.This paper is divided into two sections:Section 1: In Ref [1], 2-order ordinary differential initial value problemshave the following the superconvergence resultsand the two-point boundary value problems with singular coefficientshave the following the superconvergence resultstherefore, We have convergence results at the nodes of the linearinterpolation for 2-order ordinary differential initial value problems with singular coefficientsSection 2: In Ref[13], the intensity (E) of the electric field in the emission of laser satisfies the nonlinear Schrodinger equationIt changes to (0.1.4) with the 2-order ordinary differential problem with singular coefficients through evolution and by using the special solutionIn this paper, We only discuss the 2-order ordinary differential initial value problems with singular coefficients.Finally: we search the optimal eigenvalue β in two different ways.