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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Bibliographic Details
Published in:Computing Vol. 92; no. 3; pp. 243 - 263
Main Author: Akanbi, Moses Adebowale
Format: Journal Article
Language:English
Published: Vienna Springer Vienna 01.07.2011
Springer
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0010-485X
1436-5057
DOI:10.1007/s00607-010-0139-3