Exponentially Fitted Spline Approximation Method for Solving Selfadjoint Singular Perturbation Problems
نویسندگان
چکیده
A numerical method based on cubic spline with exponential fitting factor is given for the selfadjoint singularly perturbed two-point boundary value problems. The scheme derived in this method is second-order accurate. Numerical examples are given to support the predicted theory.
منابع مشابه
Uniformly Convergent 3-tgfem Vs Lsfem for Singularly Perturbed Convection-diffusion Problems on a Shishkin Based Logarithmic Mesh
In the present work, three-step Taylor Galerkin finite element method(3TGFEM) and least-squares finite element method(LSFEM) have been discussed for solving parabolic singularly perturbed problems. For singularly perturbed problems, a small parameter called singular perturbation parameter is multiplied with the highest order derivative term. As this singular perturbation parameter approaches to...
متن کاملAn efficient numerical method for singularly perturbed second order ordinary differential equation
In this paper an exponentially fitted finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer. A fitting factor is introduced and the model equation is discretized by a finite difference scheme on an uniform mesh. Thomas algorithm is used to solve the tri-diagonal system. The stability of the algorithm is investigated. It ...
متن کاملA Third-degree B-spline Collocation Scheme for Solving a Class of the Nonlinear Lane–-Emden Type Equations
In this paper, we use a numerical method involving collocation method with third B-splines as basis functions for solving a class of singular initial value problems (IVPs) of Lane--Emden type equation. The original differential equation is modified at the point of singularity. The modified problem is then treated by using B-spline approximation. In the case of non-linear problems, we first line...
متن کاملAn ${cal O}(h^{8})$ optimal B-spline collocation for solving higher order boundary value problems
As we know the approximation solution of seventh order two points boundary value problems based on B-spline of degree eight has only ${cal O}(h^{2})$ accuracy and this approximation is non-optimal. In this work, we obtain an optimal spline collocation method for solving the general nonlinear seventh order two points boundary value problems. The ${cal O}(h^{8})$ convergence analysis, mainly base...
متن کاملNumerical Solution of General Singular Perturbation Boundary Value Problems Based on Adaptive Cubic Spline
We use adaptive cubic spline functions to develop a numerical method for solving a class of singular perturbation two-point boundary value problems. The scheme derived in this method is second order accurate. Convergence of the method is shown. The resulting linear system of equations has been solved by using a tri-diagonal solver. Numerical examples are given to show the applicability and effi...
متن کامل