A new algorithm for nonlinear eigenvalue problems is proposed. The numerical technique is based on a perturbation of the coefficients of differential equation combined with the Adomian decomposition method for the non...
详细信息
A new algorithm for nonlinear eigenvalue problems is proposed. The numerical technique is based on a perturbation of the coefficients of differential equation combined with the Adomian decomposition method for the nonlinear part. The approach provides an exponential convergence rate with a base which is inversely proportional to the index of the eigenvalue under consideration. The eigenpairs can be computed in parallel. Numerical examples are presented to support the theory. They are in good agreement with the spectral asymptotics obtained by other authors.
In this paper we present a functional-discrete method for solving Sturm-Liouville problems with a potential that includes a function from L-1 (0, 1) and the Dirac delta-function. For both the linear and the nonlinear ...
详细信息
In this paper we present a functional-discrete method for solving Sturm-Liouville problems with a potential that includes a function from L-1 (0, 1) and the Dirac delta-function. For both the linear and the nonlinear case sufficient conditions for an exponential rate of convergence of the method are obtained. The question of a possible software implementation of the method is discussed in detail. The theoretical results are successfully confirmed by a numerical example. (C) 2013 Elsevier B.V. All rights reserved.
We consider the boundary value problems (BVPs) for linear second-order ODEs with a strongly positive operator coefficient in a Banach space. The solutions are given in the form of the infinite series by means of the C...
详细信息
We consider the boundary value problems (BVPs) for linear second-order ODEs with a strongly positive operator coefficient in a Banach space. The solutions are given in the form of the infinite series by means of the Cayley transform of the operator, the Meixner type polynomials of the independent variable, the operator Green function, and the Fourier series representation for the right-hand side of the equation. The approximate solution of each problem is a partial sum of N (or expressed through N) summands. We prove the weighted error estimates depending on the discretization parameter N, the distance of the independent variable to the boundary points of the interval, and some smoothness properties of the input data.
暂无评论