Numerical solution of a singularly perturbed two-point boundary value problem using equidistribution: analysis of convergence
نویسندگان
چکیده
منابع مشابه
Numerical solution of a singularly perturbed two-point boundary-value problem using collocation
In this paper we study a class of numerical methods to solve a singularly perturbed two-point boundary value problem. Our schemes arise as result of choosing an appropriate basis for the solution, as well as making use of collocation. It is possible to obtain arbitrarily high-order methods. We note that, in some cases (constant coefficients), we obtain the exact solution. Particular attention i...
متن کاملNumerical Solution of Singularly Perturbed Two-Point Singular Boundary Value Problems Using Differential Quadrature Method
This paper presents the application of Differential Quadrature Method (DQM) for finding the numerical solution of singularly perturbed two point singular boundary value problems. The DQM is an efficient discretization technique in solving initial and/or boundary value problems accurately using a considerably small number of grid points. This method is based on the approximation of the derivativ...
متن کاملNumerical Solution to Linear Singularly Perturbed Two Point Boundary Value Problems Using B-spline Collocation Method
A Recursive form cubic B-spline basis function is used as basis in B-spline collocation method to solve second linear singularly perturbed two point boundary value problem. The performance of the method is tested by considering the numerical examples with different boundary conditions. Results of numerical examples show the robustness of the method when compared with the analytical solution.
متن کاملConvergence Analysis of Finite-Difference Approximations of an Inhomogeneous Singularly Perturbed Boundary Value Problem Using Grid Equidistribution.
Convergence analysis of nite-diierence approximations of an inhomogeneous singularly perturbed boundary value problem using grid equidistribution. We derive-uniform error estimates for two rst-order upwind discretisations of a model inhomogeneous, second-order, singularly perturbed boundary value problem on a non-uniform grid. Here, is the small parameter multiplying the highest derivative term...
متن کاملA Numerical Scheme for Nonlinear Singularly Perturbed Two point Boundary Value Problems using Locally Exact Integration
We consider a class of nonlinear singular perturbation problems of the form [ ] β = α = ∈ = + ′ + ′ ′ ε ) ( , ) ( ]; , [ ), ( ) , ( )) ( ( ) ( b y a y b a x x r y x q x y p x y with a boundary layer at one end point. Using the theory of singular perturbations, the original problem is reduced to an asymptotically equivalent first order initial value problem. Then, a variable step size in itial v...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2000
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(99)00315-5