A difference method for non-self-adjoint singular perturbation problem of second order
نویسندگان
چکیده
منابع مشابه
Uniformly convergent non-standard finite difference methods for self-adjoint singular perturbation problems
We design non-standard finite difference schemes for self-adjoint singularly perturbed two-point boundary value problems. Essential physical properties (e.g., dissipativity) of the solutions of such problems are captured in the schemes by an appropriate renormalization of the denominator of the discrete derivative. The schemes are analyzed for -uniform convergence. Several numerical examples ar...
متن کاملA Fitted Second Order Finite Difference Method for Singular Perturbation Problems Exhibiting Dual Layers
Abstract In this paper a fitted second-order finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer at both end (left and right) points. We have introduced a fitting factor in second-order tri-diagonal finite difference scheme and it is obtained from the theory of singular perturbations. The efficient Thomas algorithm is ...
متن کاملHomoclinic orbits for second order self-adjoint difference equations
In this paper we discuss how to use variational methods to study the existence of nontrivial homoclinic orbits of the following nonlinear difference equations Δ [ p(t)Δu(t − 1)]+ q(t)u(t)= f (t, u(t)), t ∈Z, without any periodicity assumptions on p(t), q(t) and f , providing that f (t, x) grows superlinearly both at origin and at infinity or is an odd function with respect to x ∈R, and satisfie...
متن کاملHigh order fitted operator numerical method for self-adjoint singular perturbation problems
We consider self-adjoint singularly perturbed two-point boundary value problems in conservation form. Highest possible order of uniform convergence for such problems achieved hitherto, via fitted operator methods, was one (see, e.g., [Doolan et al. Uniform numerical methods for problems with initial and boundary layers, Boole Press, Dublin, 1980], p. 121]). Reducing the original problem into th...
متن کاملNON-STANDARD FINITE DIFFERENCE METHOD FOR NUMERICAL SOLUTION OF SECOND ORDER LINEAR FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS
In this article we have considered a non-standard finite difference method for the solution of second order Fredholm integro differential equation type initial value problems. The non-standard finite difference method and the composite trapezoidal quadrature method is used to transform the Fredholm integro-differential equation into a system of equations. We have also developed a numerical met...
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: Applied Mathematical Modelling
سال: 1991
ISSN: 0307-904X
DOI: 10.1016/0307-904x(91)90064-v