Nonlinear methods in solving ordinary differential equations
TLDR
Some one step methods, based on nonpolynomial approximations, for solving ordinary differential equations are derived, and numerically tested, and a comparison is made with existing methods.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 1976-01-01 and is currently open access. It has received 15 citations till now. The article focuses on the topics: Numerical methods for ordinary differential equations & Stochastic partial differential equation.read more
Citations
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Acceleration techniques for iterated vector and matrix problems : (mathematics of computation, _1_6(1962), nr 79, p 301-322)
TL;DR: In this paper, the Samelson Inverse of a Vector (SIV) is introduced, which is equivalent to the simultaneous application of the scalar e-algorithm to the components of (a), (b) and (c).
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Rational Runge-Kutta methods for solving systems of ordinary differential equations
TL;DR: To perform this, a new vector product, compatible with the Samelson inverse of a vector, is defined, and conditions for a given order are derived.
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On the stability of rational Runge Kutta methods
M Calvo,M.Mar Quemada +1 more
TL;DR: In this article, the stability of rational two-stage Runge Kutta methods for numerical solution of stiff differential systems was studied. And the necessary and sufficient conditions for the coefficients of a method to be stable were established.
Journal Article
On the Construction and Comparison of an Explicit Iterative Algorithm with Nonstandard Finite Difference Schemes
TL;DR: The proposed iterative algorithm efficiently follows the oscillatory behavior of models like Lotka-Volterra predator-prey and mass-spring system in comparison to the nonstandard schemes discussed in literature.
A New class of rational multistep methods for solving initial value problem
Teh Yuan Ying,Nazeeruddin Yaacob +1 more
TL;DR: In this paper, a new class of twostep numerical methods that are based on rational functions in solving general initial value problem and problem whose solution possesses singularity are presented. And the developments of these rational multi-step methods, as well as the local truncation error and stability analysis for each rational multistep method are presented, and they have been found out that only the second order, third order and fourth order rational multiistep methods are A-stable.
References
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Book
Introduction to approximation theory
TL;DR: In this paper, Tchebycheff polynomials and other linear families have been used for approximating least-squares approximations to systems of equations with one unknown solution.
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The Padé Table and Its Relation to Certain Algorithms of Numerical Analysis
TL;DR: Normality criteria for the Pade table, which provide existence theorems for the algorithms, are developed and possible extensions to Laurent series are indicated.