A Two-Point Series Method for Two-Point Boundary Value Problems: Theoretical Foundation
Copyright policy )A Two-Point Series Method for Two-Point Boundary Value Problems: Theoretical Foundation
A theoretical foundation is established for the numerical phase of a symbolic-numeric method for solving nonlinear, two-point, boundary value problems. The method, applicable to holomorphic systems, involves the formal (symbolic) solution of the differential system by means of two-point series. This is followed by an iterative numerical phase that produces a series satisfying the boundary value problem. Conditions are established under which the numerical phase is well defined and converges. The former problem involves the existence and local uniqueness of solutions to a constrained version of the boundary conditions and to certain initial value problems. A subsequent article will study the method as a practical computational algorithm.
Numerical solution of boundary value problems involving ordinary differential equations, Nonlinear boundary value problems for ordinary differential equations, Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
Numerical solution of boundary value problems involving ordinary differential equations, Nonlinear boundary value problems for ordinary differential equations, Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).3 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!