Results 71 to 80 of about 1,700 (198)

Innovative Approaches in Differential Equation Analysis Using the Enhanced Differential Transform and Homotopy Perturbation Method

International Journal of Differential Equations
Ordinary differential equations (ODEs) are very basic when it comes to modeling dynamic systems in various fields of science and engineering. However, solving high-dimensional, nonlinear, and stiff ODEs is still a major challenge given the limitations of
V. Murugesh, M. Priyadharshini, Yogesh Kumar Sharma, Umesh Kumar Lilhore, Sarita Simaiya, Lidia Gosy Tekeste   +5 more
doaj   +1 more source

Numerical solution for stiff initial value problems using 2-point block multistep method [PDF]

, 2018
This paper focuses on the derivation of an improved 2-point Block Backward Differentiation Formula of order five (I2BBDF(5)) for solving stiff first order Ordinary Differential Equations (ODEs). The I2BBDF(5) method is derived
Ismail, Fudziah, Ibrahim, Zarina Bibi, Mohamad Noor, N.   +2 more
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Second derivative two-step peer methods

Mathematical Modelling and Analysis
This paper is devoted to extending two-step peer methods, for the numerical solution of ordinary differential equations, for the case where the second derivative of the solution is incorporated into the formula of the methods.
Mohammad Sharifi, Ali Abdi, Michał Braś, Gholamreza Hojjati   +3 more
doaj   +1 more source

Explicit Methods for Stiff ODEs from Atmospheric Chemistry [PDF]

, 1994
The subject of research is the numerical integration of atmospheric chemical kinetics systems. The application lies in the study of air pollution, modelled by atmospheric chemistry-transport problems.
Simpson, D., J. G. Verwer, Verwer, J.G. (Jan), D. Simpson, Verwer, Jan   +4 more
core  

Benchmarking of implicit numerical integration methods for stiff unified constitutive equations in metal forming applications

Cogent Engineering
Unified constitutive equations have been developed to model the behaviour of metallic materials under various processing conditions. These constitutive equations usually take the form of a set of ordinary differential equations (ODEs), which must be ...
James Dear, Ruiqiang Zhang, Zhusheng Shi, Jianguo Lin   +3 more
doaj   +1 more source

Nonintrusive and Structure Preserving Multiscale Integration of Stiff ODEs, SDEs, and Hamiltonian Systems with Hidden Slow Dynamics via Flow Averaging [PDF]

, 2009
We introduce a new class of integrators for stiff ODEs as well as SDEs. Examples of subclasses of systems that we treat are ODEs and SDEs that are sums of two terms, one of which has large coefficients.
Jerrold E. Marsden, Tao, Molei, Houman Owhadi, Molei Tao, Marsden, Jerrold E., Owhadi, Houman   +5 more
core   +1 more source

Improved Rosenbrock method with error estimator and Jacobian approximation using complex step

Results in Applied Mathematics
This paper proposes an A-stable one-stage Rosenbrock method for the solution of Ordinary Differential Equations (ODEs). In this method, Jacobians are approximated via complex step finite differences. An asymptotically accurate estimator of the truncation
Juan Diego Pulgarín Rivera, Daniel Turizo, Elias D. Nino-Ruiz, Oscar Danilo Montoya   +3 more
doaj   +1 more source

Componentwise block partitioning: a new strategy to solve stiff ordinary differential equations [PDF]

, 2012
Componentwise Block Partitioning is a new strategy to solve stiff ODEs, based on Block Backward Differentiation Formulas (BBDFs), and block of Adam type formulas.
K. I. Othman, Z. B. Ibrahim, Ibrahim, Zarina Bibi, Othman, Khairil Iskandar   +3 more
core   +1 more source

Development of a-stable block method for the solution of stiff ordinary differential equations [PDF]

, 2019
A fixed step-size multistep block method for stiff Ordinary Differential Equations (ODEs) using the 2-point Block Backward Differentiation Formulas (BBDF) with improved efficiency is established.
Mohamad Noor, Nursyazwani, Ibrahim, Zarina Bibi   +1 more
core   +1 more source

Development of a fully implicit ODE-solver for containment analysis code

Frontiers in Energy Research
The thermal–hydraulic dynamics in containment are governed by a system of stiff ordinary differential equations (ODEs). A fully implicit discretization scheme is adopted to discretize these ODEs in order to mitigate the effects of stiffness.
Jun Huang, Jinggang Li, Yinxiang Ma
doaj   +1 more source