Journal ArticleDOI
Monte Carlo path-integral calculations for two-point boundary-value problems
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In this paper, a computational technique based on the method of path integral is studied with a view to finding approximate solutions of a class of two-point boundary-value problems, which are "rough" solutions by Monte Carlo sampling.Abstract:
A computational technique based on the method of path integral is studied with a view to finding approximate solutions of a class of two-point boundary-value problems. These solutions are "rough" solutions by Monte Carlo sampling. From the computational point of view, however, once these rough solutions are obtained for any nonlinear cases, they serve as good starting approximations for improving the solutions to higher accuracy. Numerical results of a few examples are also shown.read more
Citations
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Journal ArticleDOI
On the closed form solution of Troesch's problem
S.M Roberts,J.S Shipman +1 more
TL;DR: In this article, the closed form solution of Troesch's problem is developed in terms of Jacobian elliptic functions and two interesting properties of the closed-form solution are found: the location of a pole and branching or bifurcation behavior.
Journal ArticleDOI
Stochastic numerical treatment for solving Troesch’s problem
TL;DR: The numerical techniques are presented for the solution of Troesch’s problem based on neural networks optimized with three different methods including particle swarm optimization (PSO), active set (AS) and PSO hybridized with AS ( PSO-AS) algorithms.
Journal ArticleDOI
A variational iteration method for solving Troesch's problem
TL;DR: A new and efficient algorithm based on the variational iteration method and variable transformation is proposed to solve Troesch's problem, which is an inherently unstable two-point boundary value problem.
Book ChapterDOI
Numerical solution of boundary value problems for ordinary differential equations: survey and some recent results on difference methods
TL;DR: In this article, the numerical solution of boundary value problems for ordinary differential equations is discussed and a thorough study of truncated Chebyshev series approximations to the solution of subject to linear multi-points boundary conditions is given by Urabe.
Journal ArticleDOI
Solution of Troesch's two-point boundary value problem by a combination of techniques
S.M Roberts,J.S Shipman +1 more
TL;DR: In this paper, the authors discuss how Troesch's problem may be solved by a combination of methods, multipoint, continuation, and perturbation, although none of these methods by itself is sufficiently potent.
References
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Book
Numerical solution of differential equations
TL;DR: The program for the sixth Symposium on applied mathematics of the American Mathematical Society, on the subject of algebraic geometry, is being arranged by the Society's Applied Mathematics Committee as mentioned in this paper.
Journal ArticleDOI
The solution of nonlinear ordinary differential equations in Chebyshev series
C. W. Clenshaw,H. J. Norton +1 more
Journal ArticleDOI
Numerical solution of nonlinear two-point boundary problems by finite difference methods
TL;DR: This paper gives examples and discusses the finite difference method for nonlinear two-point boundary-value problems and the easiest method of attacking these problems, shooting techniques.
Journal ArticleDOI
Approximation of a class of Wiener integrals
TL;DR: In this article, an approximation formula for the conditional Wiener integral of the functional fix integral in Eq. (1.1 ) was derived, which may be used for machine calculations.
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