Bifurcation in Difference Approximations to Two-Point Boundary Value Problems

Bifurcation in Difference Approximations to Two-Point Boundary Value Problems

Numerical methods for bifurcation problems of the form (*) Ly = Xf(y), By = 0, where/(0) = 0 and /'(0) ^ 0, are considered. Here y is a scalar function, A. is a real scalar, L is a linear differential operator and By = 0 represents some linear homogeneous two-point boundary conditions. Under certain assumptions, it is shown that if (*) is replaced by an appropriate difference scheme, then there...

Chebyshev finite difference method for a two−point boundary value problems with applications to chemical reactor theory

In this paper, a Chebyshev finite difference method has been proposed in order to solve nonlinear two-point boundary value problems for second order nonlinear differential equations. A problem arising from chemical reactor theory is then considered. The approach consists of reducing the problem to a set of algebraic equations. This method can be regarded as a non-uniform finite difference schem...

B-SPLINE METHOD FOR TWO-POINT BOUNDARY VALUE PROBLEMS

In this work the collocation method based on quartic B-spline is developed and applied to two-point boundary value problem in ordinary diferential equations. The error analysis and convergence of presented method is discussed. The method illustrated by two test examples which verify that the presented method is applicable and considerable accurate.

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation

Tridiagonal Fourth Order Approximations to General Two-Point Nonlinear Boundary Value Problems with Mixed Boundary Conditions

This paper develops fourth order discretizations to the two-point boundary value problem y(2kt)=f(t,y(t),y(1\t)), ^o^0) "o^(1)(°) = 60' al ?W + "l^1^1) = 5 1These discretizations have the desirable properties that they are tridiagonal and of "positive type".