scholarly journals Exponentially fitted two-derivative DIRK methods for oscillatory differential equations

2022 ◽  
Vol 418 ◽  
pp. 126770
Author(s):  
Julius O. Ehigie ◽  
Vu Thai Luan ◽  
Solomon A. Okunuga ◽  
Xiong You
Keyword(s):  
Differential Equations ◽  
Exponentially Fitted ◽  
Dirk Methods

Exponentially fitted symmetric and symplectic DIRK methods for oscillatory Hamiltonian systems

2017 ◽  
Vol 56 (4) ◽  
pp. 1130-1152
Author(s):  
Julius Osato Ehigie ◽  
Dongxu Diao ◽  
Ruqiang Zhang ◽  
Yonglei Fang ◽  
Xilin Hou ◽  
...  
Keyword(s):  
Hamiltonian Systems ◽  
Oscillatory Hamiltonian Systems ◽  
Exponentially Fitted ◽  
Dirk Methods

scholarly journals A FAMILY OF EXPONENTIALLY FITTED MULTIDERIVATIVE METHOD FOR STIFF DIFFERENTIAL EQUATIONS

2017 ◽  
Vol 13 (2) ◽  
pp. 7155-7162
Author(s):  
Abhulimen Cletus ◽  
Ukpebor L a
Keyword(s):  
Differential Equations ◽  
Numerical Stability ◽  
Multistep Method ◽  
Stiff Differential Equations ◽  
Derivative Method ◽  
Numerical Stability Analysis ◽  
Exponentially Fitted ◽  
Free Parameters ◽  
Predictor Corrector ◽  
Third Derivative

In this paper, an A-stable exponentially fitted predictor-corrector using multiderivative linear multistep method for solving stiff differential equations is developed. The method which is a two-step third derivative method of order five contains free parameters. The numerical stability analysis of the method was discussed, and found to be A-stable. Numerical examples are provided to show the efficiency of the method when compared with existing methods in the literature that have solved the set of problems.

scholarly journals A Numerical Technique for Solving Nonlinear Singularly Perturbed Delay Differential Equations

2018 ◽  
Vol 23 (1) ◽  
pp. 64-78 ◽  
Author(s):  
A.S.V. Ravi Kanth ◽  
P. Murali Mohan Kumar
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Numerical Technique ◽  
Singularly Perturbed ◽  
Spline Method ◽  
Numerical Examples ◽  
Exponentially Fitted ◽  
Delay Differential ◽  
Quasilinearization Technique

This paper presents a numerical technique for solving nonlinear singu- larly perturbed delay differential equations. Quasilinearization technique is applied to convert the nonlinear singularly perturbed delay differential equation into a se- quence of linear singularly perturbed delay differential equations. An exponentially fitted spline method is presented for solving sequence of linear singularly perturbed delay differential equations. Error estimates of the method is discussed. Numerical examples are solved to show the applicability and efficiency of the proposed scheme.

scholarly journals Novel Exponentially Fitted Two-Derivative Runge-Kutta Methods with Equation-Dependent Coefficients for First-Order Differential Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Yanping Yang ◽  
Yonglei Fang ◽  
Xiong You ◽  
Bin Wang
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Numerical Results ◽  
First Order ◽  
Truncation Errors ◽  
New Methods ◽  
Exponentially Fitted ◽  
Runge Kutta ◽  
First Order Differential Equations

The construction of exponentially fitted two-derivative Runge-Kutta (EFTDRK) methods for the numerical solution of first-order differential equations is investigated. The revised EFTDRK methods proposed, with equation-dependent coefficients, take into consideration the errors produced in the internal stages to the update. The local truncation errors and stability of the new methods are analyzed. The numerical results are reported to show the accuracy of the new methods.

Exponentially fitted difference scheme for singularly perturbed mixed integro-differential equations

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Musa Cakir ◽  
Baransel Gunes
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Difference Scheme ◽  
Singularly Perturbed ◽  
Stability And Convergence ◽  
Uniform Mesh ◽  
Numerical Examples ◽  
Exponentially Fitted ◽  
The Stability ◽  
Exponentially Fitted Difference Scheme

Abstract In this study, singularly perturbed mixed integro-differential equations (SPMIDEs) are taken into account. First, the asymptotic behavior of the solution is investigated. Then, by using interpolating quadrature rules and an exponential basis function, the finite difference scheme is constructed on a uniform mesh. The stability and convergence of the proposed scheme are analyzed in the discrete maximum norm. Some numerical examples are solved, and numerical outcomes are obtained.

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