The Finite Volume Element Method Based On Improved Grade Mesh For Solving Nonlinear Singularly Perturbed Two-point Boundary Value Problems

It is necessary to study the solution of singularly perturbed two-point boundary value problems,because they appear in all fields of natural science.The thesis based on the method of finite volume element on improved grade mesh studies the solution of singularly perturbed two-point boundary value problems,and compares with the Shishkin mesh.The thesis discusses three kinds of singularly perturbed two-point boundary value problems from simple to complex.Firstly,the thesis studies the finite volume element method based on improved grade mesh of linear singularly perturbed two-point boundary value problems to get the corresponding calculation scheme.What's more,discussing the error estimation and convergence of the finite volume element method and verifying the validity of the finite volume element method by a numerical example.Secondly,the thesis studies the semilinear singularly perturbed two-point boundary value problem based on the finite volume element calculation scheme with interpolation coefficients and gets the specific calculation scheme by Newton iterative method to discuss the corresponding error estimation and convergence.Finally,the thesis studies the nonlinear singularly perturbed two-point boundary value problem by using Taylor expansion to transform it into the semilinear singularly perturbed two-point boundary value problem,then solving the corresponding calculation scheme and proving that the nonlinear singularly perturbed two-point boundary value problem has the same convergence as the semilinear singularly perturbed two-point problem.