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 New L-Stable Third Derivative Hybrid Method for Solving First Order Ordinary Differential Equations

2021 ◽  
pp. 58-69
Author(s):  
Lawrence Osa Adoghe
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Hybrid Method ◽  
Multistep Method ◽  
Stability And Convergence ◽  
Stiff Systems ◽  
Convergence Properties ◽  
Main Method ◽  
The Stability ◽  
Third Derivative

In this paper, an L-stable third derivative multistep method has been proposed for the solution of stiff systems of ordinary differential equations. The continuous hybrid method is derived using interpolation and collocation techniques of power series as the basis function for the approximate solution. The method consists of the main method and an additional method which are combined to form a block matrix and implemented simultaneously. The stability and convergence properties of the block were investigated and discussed. Numerical examples to show the efficiency and accuracy of the new method were presented.

scholarly journals A Seven-Step Block Multistep Method for the Solution of First Order Stiff Differential Equations

2020 ◽  
Vol 12 (1) ◽  
pp. 72-82
Author(s):  
Solomon Gebregiorgis ◽  
Hailu Muleta
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Power Series ◽  
Differential Equations ◽  
Multistep Method ◽  
Stiff Differential Equations ◽  
Block Method ◽  
Initial Value ◽  
Numerical Examples ◽  
First Order

In this paper, a seven-step block method for the solution of first order initial value problem in ordinary differential equations based on collocation of the differential equation and interpolation of the approximate solution using power series have been formed. The method is found to be consistent and zero-stable which guarantees convergence. Finally, numerical examples are presented to illustrate the accuracy and effectiveness of the method.  Keywords: Power series, Collocation, Interpolation, Block method, Stiff.

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