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Stability improvement of the Euler forward method for initial value problems
Author(s) -
Kujawski Jerzy
Publication year - 1988
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690040405
Subject(s) - mathematics , stability (learning theory) , euler's formula , backward euler method , relaxation (psychology) , nonlinear system , transient (computer programming) , matrix (chemical analysis) , euler method , finite element method , euler equations , value (mathematics) , mathematical analysis , computer science , thermodynamics , physics , psychology , social psychology , statistics , materials science , quantum mechanics , machine learning , composite material , operating system
The Euler forward method is transformed into a highly stable two‐step explicit algorithm by use of a relaxation paramenter α. The stability of the new explicit family can be very high and linearly proportional to the absolute value of α. An adaptive stability approach with a matrix of parameters α is used that strongly increases the effeciency of the method. The one‐dimensional finite element solutions for linear and nonlinear transient heat conduction problems show the stability, accuracy, and computational efficiency characteristics of the proposed algorithms.