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Implicit numerical methods for stiff stochastic differential equations and numerical simulations of stochastic models

2019
In this thesis efficient implicit numerical methods are constructed for solving stochastic differential equations and numerical simulations are presented for stochastic models in environmental modelling and mathematical finance. Two types of stochastic differential equations are discussed in this thesis: Itô and Stratonovich.
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A class of numerical methods for stiff systems of ordinary differential equations

1987
Summary: We propose a class of second derivative multistep methods suitable for the approximate numerical integration of stiff systems of first order ordinary differential equations. In the case \(K=1\), we obtain a class of fifth order L-stable method. In the case \(K=2\), we obtain an eight order stiff-stable method.
openaire   +2 more sources

Study of Numerical Solutions of Stiff Differential Equations Using Rk Method and Adaptive Stepsize Control Method

Communications on Applied Nonlinear Analysis
In this paper, chemical kinetics, electrical circuits, and spring-damping systems, stiff differential equations are specialized initial value issues. Numerical methods are needed for accurate computations because most practical stiff systems lack analytical solutions because to their complexity.
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Review Paper: Efficient numerical methods for the solution of stiff initial-value problems and differential algebraic equations

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2003
J R Cash
exaly  

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