On 3-stage geometric explicit Runge–Kutta method for singular autonomous initial value problems in ordinary differential equations

There has been considerable efforts to increase the efficiency of explicit Runge–Kutta (ERK) methods over the years. However, this always lead to increase in the number of terms of the Taylors’ series incremental function. In this work, a 3-stage geometric explicit Runge–Kutta method for solving aut...

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Vydáno v:	Computing Ročník 92; číslo 3; s. 243 - 263
Hlavní autor:	Akanbi, Moses Adebowale
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Vienna Springer Vienna 01.07.2011 Springer Springer Nature B.V
Témata:	Algorithmics. Computability. Computer arithmetics Algorithms Applied sciences Artificial Intelligence Autonomous Computation Computer Appl. in Administrative Data Processing Computer Communication Networks Computer Science Computer science; control theory; systems Differential equations Exact sciences and technology Information Systems Applications (incl.Internet) Initial value problems Mathematical analysis Mathematical models Mathematics Methods Methods of scientific computing (including symbolic computation, algebraic computation) Numerical analysis Numerical analysis. Scientific computation Ordinary differential equations Partial differential equations, initial value problems and time-dependant initial-boundary value problems Runge-Kutta method Sciences and techniques of general use Software Engineering Studies Theoretical computing 65L05 65L06 Geometric explicit Runge–Kutta method Stability 65L20 Singular initial value problems Algorithm Absolute stability Convergence Differential equation Initial value problem Singular value Taylor series Runge Kutta method Partial differential equation Implementation Extrapolation Numerical analysis Scientific computation Multistep method Geometric explicit Runge-Kutta method Numerical stability
ISSN:	0010-485X, 1436-5057
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Shrnutí:	There has been considerable efforts to increase the efficiency of explicit Runge–Kutta (ERK) methods over the years. However, this always lead to increase in the number of terms of the Taylors’ series incremental function. In this work, a 3-stage geometric explicit Runge–Kutta method for solving autonomous initial value problems in ordinary differential equations is derived and implemented. The computational results show that the method is stable, efficient and accurate. We also compared this method with some other conventional methods.
Bibliografie:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23
ISSN:	0010-485X 1436-5057
DOI:	10.1007/s00607-010-0139-3