The Numerical Solution of Stiff IVPs in ODEs Using Modified Second Derivative BDF [PDF]
, 2012 summary:This paper considers modified second derivative BDF (MSD-BDF) for the numerical solution of stiff initial value problems (IVPs) in ordinary differential equations (ODEs). The methods are A$(\alpha )$-stable for step length $k\le 7$
Ikhile, M. N. O., Okuonghae, R. I.
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Continuous Runge–Kutta schemes for pantograph type delay differential equations
Partial Differential Equations in Applied MathematicsPantograph differential equations are important types of delay differential equations. Using continuous mono-implicit RK schemes, we propose a numerical method for numerically approximating pantograph delay differential equations that are reliable and ...
Fathalla A. Rihan
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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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Almost sure exponential stability of numerical solutions for stochastic delay differential equations
, 2010 Using techniques based on the continuous and discrete semimartingale convergence theorems, this paper investigates if numerical methods may reproduce the almost sure exponential stability of the exact solutions to stochastic delay differential equations (
Szpruch, Lukasz, Wu, Fuke, Mao, Xuerong
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Efficient simulation of stochastic chemical kinetics with the Stochastic Bulirsch-Stoer extrapolation method [PDF]
, 2014 BackgroundBiochemical systems with relatively low numbers of components must be simulated stochastically in order to capture their inherent noise. Although there has recently been considerable work on discrete stochastic solvers, there is still a need ...
Barrio Solórzano, Manuel +11 more
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Super class of implicit extended backward differentiation formulae for the numerical integration of stiff initial value problems [PDF]
Computational Algorithms and Numerical DimensionsAn implicit Superclass of non-block Extended Backward Differentiation Formulae (SEBDF) for the numerical integration of first-order stiff system of Ordinary Differential Equations (ODEs) in Initial Value Problems (IVPs) with optimal stability properties ...
Hamisu Musa, Buhari Alhassan
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Mathematics, 2022 Mathematical models, some of which incorporate both intracellular and extracellular hepatitis C viral kinetics, have been advanced in recent years for studying HCV–host dynamics, antivirals mode of action, and their efficacy.
Vladimir Reinharz +3 more
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Explicit methods for stiff stochastic differential equations [PDF]
, 2011 Multiscale differential equations arise in the modeling of many important problems in the science and engineering. Numerical solvers for such problems have been extensively studied in the deterministic case.
Assyr Abdulle, Abdulle, Assyr
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High order boundary value linear multistep method for the numerical solution of IVPs in ODEs
Journal of Nigerian Society of Physical SciencesIn this paper, we introduce High order boundary value linear multistep method (HOBVLMM) for the numerical solution of stiff systems of initial value problems (IVPs).
Seun Ogunfeyitimi +2 more
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Numerical methods for extremely stiff systems of ordinary differential equations
Applied Mathematical Modelling, 1979 Computer simulation of dynamic systems very often leads to the solution of a set of stiff ordinary differential equations. The solution of this set of equations involves the eigenvalues of its Jacobian matrix. The greater the spread in eigenvalues, the more time consuming the solutions become when existing numerical methods are employed.
Bui, T. D., Bui, T. R.
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