Results 1 to 10 of about 1,109 (164)
A novel hybrid framework for efficient higher order ODE solvers using neural networks and block methods [PDF]
Scientific ReportsIn this paper, the author introduces the Neural-ODE Hybrid Block Method, which serves as a direct solution for solving higher-order ODEs. Many single and multi-step methods employed in numerical approximations lose their stability when applied in the ...
V. Murugesh +7 more
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Explicit Time-Stepping for Stiff ODEs [PDF]
SIAM Journal of Scientific Computing, 2004 We present a new strategy for solving stiff ODEs with explicit methods. By adaptively taking a small number of stabilizing small explicit time steps when necessary, a stiff ODE system can be stabilized enough to allow for time steps much larger than what is indicated by classical stability analysis.
Kenneth Eriksson +2 more
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Gauss–Seidel Iteration for Stiff ODES from Chemical Kinetics [PDF]
SIAM Journal of Scientific Computing, 1994 Summary: A simple Gauss-Seidel technique is proposed that exploits the special form of the chemical kinetics equations. Classical Aitken extrapolation is applied to accelerate convergence. The technique is meant for implementation in stiff solvers that are used in long range transport air pollution codes using operator splitting.
J G Verwer
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Ill-conditioned matrices and the integration of stiff ODEs
Journal of Computational and Applied Mathematics, 1993 The article is concerned with the numerical integration of stiff initial value problems for systems of ordinary differential equations. It is shown that the matrices occurring in the linear algebraic systems, which have to be solved when implicit linear multistep methods are applied, are ``almost always'' very ill-conditioned.
Lawrence F Shampine
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UMYU Scientifica Journal, 2022 In many fields of study such as science and engineering, various real life problems are created as mathematical models before they are solved. These models often lead to special class of ordinary differential equations known as stiff ODEs.
Najamuddeen Bala, Hamisu Musa
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Haar wavelet collocation method for linear first order stiff differential equations [PDF]
ITM Web of Conferences, 2020 In general, there are countless types of problems encountered from different disciplines that can be represented by differential equations. These problems can be solved analytically in simpler cases; however, computational procedures are required for more ...
Atay Mehmet Tarık +4 more
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Enhancing Accuracy of Runge–Kutta-Type Collocation Methods for Solving ODEs
Mathematics, 2021 In this paper, a new class of Runge–Kutta-type collocation methods for the numerical integration of ordinary differential equations (ODEs) is presented. Its derivation is based on the integral form of the differential equation.
Janez Urevc, Miroslav Halilovič
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Mathematics, 2020 Recently, block backward differentiation formulas (BBDFs) are used successfully for solving stiff differential equations. In this article, a class of hybrid block backward differentiation formulas (HBBDFs) methods that possessed A –stability are ...
Zarina Bibi Ibrahim +1 more
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Adaptive integration of stiff ODE
Informatica, 2000 Summary: The accuracy of adaptive integration algorithms for solving stiff ordinary differential equations (ODEs) is investigated. The analysis is done by comparing the discrete and exact amplification factors of the equations. It is proved that the usage of stiffness number of the Jacobian matrix is sufficient in order to estimate the complexity of ...
Čiegis, Raimondas +2 more
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Multirate Numerical Integration for Stiff ODEs [PDF]
, 2010 This paper contains an overview of a self-adjusting multirate method. A simple extension which allows the improvement of the efficiency of the method is introduced. The performance of the extended and the original method is compared for a test problem.
Savcenco, V., Mattheij, R.M.M.
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