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For an overview of this method for ordinary differential equations, the reader is referred to [7].
In this paper, the Jacobi spectral method for ordinary differential equations, which is based on the Jacobi approximation with negative integer, is proposed.
A numerical method for ordinary differential equations modeling the movement of the discontinuity curve is incorporated into the algorithm to compute discontinuity positions.
Employing Laplace transform techniques and series solving method for ordinary differential equation, solutions for the time-dependent temperature and thermo-mechanical stresses are obtained.
Specifically, we formulate a parallel algorithm to generate the sample path of nonlinear oscillator defined by stochastic differential equations (SDEs) using the so-called parareal method for ordinary differential equations (ODEs).
In this study, the proposed algorithm is derived from the Runge Kutta method for ordinary differential equations.
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The papers [1 5] focus on the numerical methods for ordinary differential equations.
These methods are an extension of the weighted average methods for ordinary (non-fractional) diffusion equations.
We discuss error propagation for general linear methods for ordinary differential equations up to terms of order p+2, where p is the order of the method.
Bellen and Zennaro [11] gave the theoretical aspects of numerical methods for ordinary and delay differential equations, and suitable techniques for solving numerically such type of equations.
It is known that delay differential equations can be solved by applying standard numerical methods for ordinary differential equations without the presence of delay.
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