Runge-Kutta Nystrom Method of Order Three for Solving Fuzzy Differential Equations

Kanagarajan, K.; Sambath, M.

doi:10.2478/cmam-2010-0011

Cited by 9 publications

(6 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The convergence of Euler's method is considered by (Kanagarajan and Sambath, 2010) to improve the ODE problem in a higher convergence of order O(h 3 ) (Ma et al, 1999). It was a development over (Abbasbandy and Viranloo, 2002) algorithms to solve fuzzy based differential (Seikkala, 1987).…”

Section: Runge-kutta Methodsmentioning

confidence: 99%

Computational Techniques Based on Runge-Kutta Method of Various Order and Type for Solving Differential Equations

Chauhan

Srivastava

2019

Int J Math, Eng, Manag Sci

View full text Add to dashboard Cite

The Runge-Kutta method is a one step method with multiple stages, the number of stages determine order of method. The method can be applied to work out on differential equation of the type’s explicit, implicit, partial and delay differential equation etc. The present paper describes a review on recent computational techniques for solving differential equations using Runge-Kutta algorithm of various order. This survey includes the summary of the articles of last decade till recent years based on third; fourth; fifth and sixth order Runge-Kutta methods. Along with this a combination of these methods and various other type of Runge-Kutta algorithm based articles are included. Comparisons of methods with own critical comments as remarks have been included.

show abstract

Section: Runge-kutta Methodsmentioning

confidence: 99%

Computational Techniques Based on Runge-Kutta Method of Various Order and Type for Solving Differential Equations

Chauhan

Srivastava

2019

Int J Math, Eng, Manag Sci

View full text Add to dashboard Cite

show abstract

“…In [44] a numerical algorithm in order to solve FDEs on the basis of Seikkala's derivative of a fuzzy process is suggested. A numerical technique based on a Runge-Kutta Nystrom technique of order three is employed for solving the initial value problem, also it is illustrated that this methodology is superior in comparison with the Euler method by considering the convergence order of Euler methodology (O(h)) as well as Runge-Kutta Nystrom methodology (O(h 3 )).…”

Section: Runge-kutta Methodsmentioning

confidence: 99%

Fuzzy Control of Uncertain Nonlinear Systems with Numerical Techniques: A Survey

Jafari

Razvarz

Gegov

et al. 2019

Advances in Intelligent Systems and Computing

View full text Add to dashboard Cite

This paper provides an overview of numerical methods in order to solve fuzzy equations (FEs). It focuses on different numerical methodologies to solve FEs, dual fuzzy equations (DFEs), fuzzy differential equations (FDEs) and partial fuzzy differential equations (PFDEs). The solutions which are produced by these equations are taken to be the controllers. This paper also analyzes the existence of the roots of FEs and some important implementation problems. Finally, several examples are reviewed with different methods.

show abstract

“…The form of this method is given (Sharp et al (1990), Van de Houwen and Sommeijer (1989), Franco and Gomez (2009)) by In the literature, several high-order diagonally implicit Runge-Kutta-Nystrom (DIRKN) methods have been proposed for the integration of the IVP (1) on one-processor computers. For example, the two-stage and three-stage DIRKN methods orders three and four of Sharp et al (1990), the two-stage DIRKN methods of order four of Sommeijer (1987), DIRKN methods for oscillatroty problems by Van der Houwen and Sommeijer (1989), the RKN methods of orders three for solving fuzzy differential equations of Kanagarajam and Sambath (2010). However, parallel IVP solvers arise from the need to solve many substantial problems faster than is currently possible.…”

Section: Introductionmentioning

confidence: 99%

A Diagonally Implicit Runge-Kutta-Nystrom (Rkn) Method for Solving Second Order Odes on Parallel Computers

Imoni

2020

FJS

View full text Add to dashboard Cite

In this paper, diagonally implicit Runge-Kutta-Nystrom (RKN) method of high-order for the numerical solution of second order ordinary differential equations (ODE) possessing oscillatory solutions to be used on parallel computers is constructed. The method has the properties of minimized local truncation error coefficients as well as possessing non-empty interval of periodicity, thus suitable for oscillatory problems. The method was tested with standard test problems from the literature and numerical results compared with the analytical solution to show the advantage of the algorithm

show abstract

Runge-Kutta Nystrom Method of Order Three for Solving Fuzzy Differential Equations

Cited by 9 publications

References 14 publications

Computational Techniques Based on Runge-Kutta Method of Various Order and Type for Solving Differential Equations

Computational Techniques Based on Runge-Kutta Method of Various Order and Type for Solving Differential Equations

Fuzzy Control of Uncertain Nonlinear Systems with Numerical Techniques: A Survey

A Diagonally Implicit Runge-Kutta-Nystrom (Rkn) Method for Solving Second Order Odes on Parallel Computers

Contact Info

Product

Resources

About