A new approach to the problem of constructing recurrence relations for the Jacobi coefficients
A Note on C° Galerkin Methods for Two-Point Boundary Problems.
A numerical method for a singularly perturbed three-point boundary value problem.
A Numerical Method for Solving Singular Boundary Value Problems.
A Numerical Method to Boundary Value Problems for Second Order Delay Differential Equations.
A Petrov-Galerkin approximation of convection-diffusion and reaction-diffusion problems
A general construction of test functions in the Petrov-Galerkin method is described. Using this construction; algorithms for an approximate solution of the Dirichlet problem for the differential equation are presented and analyzed theoretically. The positive number is supposed to be much less than the discretization step and the values of . An algorithm for the corresponding two-dimensional problem is also suggested and results of numerical tests are introduced.
A posteriori error estimation for arbitrary order FEM applied to singularly perturbed one-dimensional reaction-diffusion problems
FEM discretizations of arbitrary order are considered for a singularly perturbed one-dimensional reaction-diffusion problem whose solution exhibits strong layers. A posteriori error bounds of interpolation type are derived in the maximum norm. An adaptive algorithm is devised to resolve the boundary layers. Numerical experiments complement our theoretical results.
A Refinement Process for Collocation Approximations.
A remark on a class of universal hill functions
A Stepsize Control for Continuation Methods and its Special Application to Multiple Shooting Techniques.
A Taylor Series Method for the Numerical Solution of Two-Point Boundary Value Problems.
A Two Point Boundary Value Problem with a Rapidly Oscillating Solution.
A unified approach to singular problems arising in the membrane theory
We consider the singular boundary value problem where is a given continuous function defined on the set which can have a time singularity at and a space singularity at . Moreover, , , and , , are real constants such that , whereas . The main aim of this paper is to discuss the existence of solutions to the above problem and apply the general results to cover certain classes of singular problems arising in the theory of shallow membrane caps, where we are especially interested in...
A Uniformly Convergent Difference Scheme for a Semilinear Singular Perturbation Problem.
A uniformly convergent quadratic spline difference scheme for singular perturbation problems
A well-posed shooting method for transferable DAE's.
Accurate WKB Approximation for a 1D Problem with Low Regularity
2000 Mathematics Subject Classification: 34L40, 65L10, 65Z05, 81Q20.This article is concerned with the analysis of the WKB expansion in a classically forbidden region for a one dimensional boundary value Schrodinger equation with a non smooth potential. The assumed regularity of the potential is the one coming from a non linear problem and seems to be the critical one for which a good exponential decay estimate can be proved for the first remainder term. The treatment of the boundary conditions brings...
Affine-invariant monotone iteration methods with application to systems of nonlinear two-point boundary value problems
In this paper we present a new theorem for monotone including iteration methods. The conditions for the operators considered are affine-invariant and no topological properties neither of the linear spaces nor of the operators are used. Furthermore, no inverse-isotony is demanded. As examples we treat some systems of nonlinear ordinary differential equations with two-point boundary conditions.
Algorithm 47. Solution of a first-order non-linear differential equation in Chebyshev series
An Analysis and Improvement of the El~mistikawy and Werle Scheme