
An Effective and Efficient Method to Solve the HighOrder and the NonLinear Ordinary Differential Equations: the Ratio Net
An effective and efficient method that solves the highorder and the non...
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A FeynmanKac Type Theorem for ODEs: Solutions of Second Order ODEs as Modes of Diffusions
In this article, we prove a FeynmanKac type result for a broad class of...
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On the Globalization of ASPIN Employing TrustRegion Control Strategies – Convergence Analysis and Numerical Examples
The parallel solution of large scale nonlinear programming problems, wh...
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An algorithm based on continuation techniques for minimization problems with highly nonlinear equality constraints
We present an algorithm based on continuation techniques that can be app...
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New Development of Homotopy Analysis Method for a Nonlinear IntegroDifferential Equations with initial conditions
Homotopy analysis method (HAM) was proposed by Liao in 1992 in his PhD t...
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A Technical Note: TwoStep PECE Methods for Approximating Solutions To First and SecondOrder ODEs
Twostep predictor/corrector methods are provided to solve three classes...
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Sundials/ML: Connecting OCaml to the Sundials Numeric Solvers
This paper describes the design and implementation of a comprehensive OC...
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A discussion on the approximate solutions of first order systems of nonlinear ordinary equations
We develop a one step matrix method in order to obtain approximate solutions of first order systems and nonlinear ordinary differential equations, reducible to first order systems. We find a sequence of such solutions that converge to the exact solution. We study the precision, in terms of the local error, of the method by applying it to different well known examples. The advantage of the method over others widely used lies on the simplicity of its implementation.
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