Numerical Method Of Quasilinear Singularly Perturbed Two Point Boundary Value Problems Based On Equidistribution

In this paper,an adaptive numerical method based on equal distribution principle for Quasilinear Singularly perturbed two-point boundary value problems and its error analysis are discussed.In order to prove the stability between infinite norm and * norm of the quasilinear operator,we introduce a linear operator which has a special transformation relationship with the quasilinear operator.By using the properties of Green's function and its solution of linear operators,the bounds of Green's function corresponding to linear operators are obtained by comparison principle.Then,according to the property that the associated operator of inner product is M-matrix,the piecewise monotonicity of Green's function by linear operator is proved.The stability between infinite norm and * norm of the linear operator is proved by inequalities.Finally,the required stability is obtained through the relationship between the linear operator and the quasi linear operator.On any grid,we give the midpoint upwind difference scheme.By using the property of the inequality,we can get the posterior error estimate of the midpoint upwind difference scheme.On the non-uniform adaptive grid with uniformly distributed arc length control function,we use the midpoint upwind difference scheme to discretize the introduced linear operator.The discrete linear operator and quasi linear operator still have the transformation relationship.By using the properties of discrete Green's function,we prove the boundedness of the arc length of the numerical solution and obtain the conclusion from the posterior error estimation.Finally,the first order uniform convergence of the adaptive midpoint upwind scheme based on arc-length equidistribution with respect to small perturbation parameters can be proved.Finally,numerical experiments are carried out,and the error analysis is confirmed.