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Numerical solution of inhomogeneous and non‐linear ordinary differential equations using the TLM multicompartment model
Author(s) -
Saleh A. H. M.,
De Cogan D.
Publication year - 1990
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/jnm.1660030306
Subject(s) - numerical partial differential equations , ordinary differential equation , exponential integrator , mathematics , differential algebraic equation , backward differentiation formula , numerical methods for ordinary differential equations , independent equation , differential equation , examples of differential equations , explicit and implicit methods , simultaneous equations , linear differential equation , delay differential equation , numerical analysis , simple (philosophy) , mathematical analysis , reduction of order , philosophy , epistemology
The paper presents a simple algorithm for solving a system of inhomogeneous high order differential equations with variable coefficients. The method also provides a numerical solution to non‐linear ordinary differential equations. The technique is based on reducing the high order equations into a system of first order rate equations. Through a simple translation process, the variables in the reduced set of equations are solved simultaneously by an iterative scheme using the TLM multicompartment model. The numerical technique is demonstrated by solving well‐known second order differential equations. The numerical solutions are compared with the analytical solutions to the differential equations.