scholarly journals Adam-Bash forth-Multan Predictor Corrector Method for Solving First Order Initial value problem and Its Error Analysis

2021 ◽  
Vol 1 (2) ◽  
pp. 30-40
Author(s):  
Kedir Aliyi Koroche ◽  
Geleta Kinkino Mayu
Keyword(s):  
Fourth Order ◽  
Initial Value Problem ◽  
Present Method ◽  
Numerical Scheme ◽  
Mesh Size ◽  
Stability And Convergence ◽  
Initial Value ◽  
Finite Difference Approximations ◽  
The Stability ◽  
Predictor Corrector

This paper presents fourth order Adams predictor corrector numerical scheme for solving initial value problem. First, the solution domain is discretized. Then the derivatives in the given initial value problem are replaced by finite difference approximations and the numerical scheme that provides algebraic systems of difference equations is developed. The starting points are obtained by using fourth order Runge-Kutta method and then applying the present method to finding the solution of Initial value problem. To validate the applicability of the method, two model examples are solved for different values of mesh size. The stability and convergence of the present method have been investigated. The numerical results are presented by tables and graphs. The present method helps us to get good results of the solution for small value of mesh size h. The proposed method approximates the exact solution very well. Moreover, the present method improves the findings of some existing numerical methods reported in the literature.

scholarly journals Adam-Bash forth-Multan Predictor Corrector Method for Solving First Order Initial value problem and Its Error Analysis

2021 ◽  
pp. 30-40
Author(s):  
Kedir Aliyi Koroche ◽  
◽  
Geleta Kinkino Mayu ◽  
Keyword(s):  
Fourth Order ◽  
Initial Value Problem ◽  
Present Method ◽  
Numerical Scheme ◽  
Mesh Size ◽  
Stability And Convergence ◽  
Initial Value ◽  
Finite Difference Approximations ◽  
The Stability ◽  
Predictor Corrector

This paper presents fourth order Adams predictor corrector numerical scheme for solving initial value problem. First, the solution domain is discretized. Then the derivatives in the given initial value problem are replaced by finite difference approximations and the numerical scheme that provides algebraic systems of difference equations is developed. The starting points are obtained by using fourth order Runge-Kutta method and then applying the present method to finding the solution of Initial value problem. To validate the applicability of the method, two model examples are solved for different values of mesh size. The stability and convergence of the present method have been investigated. The numerical results are presented by tables and graphs. The present method helps us to get good results of the solution for small value of mesh size h. The proposed method approximates the exact solution very well. Moreover, the present method improves the findings of some existing numerical methods reported in the literature.

Improved Predictor Corrector Method for solving fuzzy initial value problem

2009 ◽  
Author(s):  
T. Allahviranloo ◽  
N. Ahmady ◽  
E. Ahmady ◽  
Alberto Cabada ◽  
Eduardo Liz ◽  
...  
Keyword(s):  
Initial Value Problem ◽  
Initial Value ◽  
Predictor Corrector

scholarly journals Numerical Study on Phase-Fitted and Amplification-Fitted Diagonally Implicit Two Derivative Runge-Kutta Method for Periodic IVPS

2021 ◽  
Vol 50 (6) ◽  
pp. 1799-1814
Author(s):  
Norazak Senu ◽  
Nur Amirah Ahmad ◽  
Zarina Bibi Ibrahim ◽  
Mohamed Othman
Keyword(s):  
Fourth Order ◽  
Initial Value Problems ◽  
Numerical Experiments ◽  
Numerical Study ◽  
Kutta Method ◽  
Initial Value ◽  
First Order ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
The Stability

A fourth-order two stage Phase-fitted and Amplification-fitted Diagonally Implicit Two Derivative Runge-Kutta method (PFAFDITDRK) for the numerical integration of first-order Initial Value Problems (IVPs) which exhibits periodic solutions are constructed. The Phase-Fitted and Amplification-Fitted property are discussed thoroughly in this paper. The stability of the method proposed are also given herewith. Runge-Kutta (RK) methods of the similar property are chosen in the literature for the purpose of comparison by carrying out numerical experiments to justify the accuracy and the effectiveness of the derived method.

scholarly journals The influence of circulation on the stability of vortices to mode-one disturbances

1995 ◽  
Vol 451 (1943) ◽  
pp. 747-755 ◽  
Keyword(s):  
Velocity Field ◽  
Angular Velocity ◽  
Initial Value Problem ◽  
Large Time ◽  
Asymptotic Methods ◽  
Two Dimensional ◽  
Initial Value ◽  
The Stability ◽  
Ultimate Fate ◽  
Solution Behaviour

The initial value problem for the two-dimensional inviscid vorticity equation, linearized about an azimuthal basic velocity field with monotonic angular velocity, is solved exactly for mode-one disturbances. The solution behaviour is investigated for large time using asymptotic methods. The circulation of the basic state is found to govern the ultimate fate of the disturbance: for basic state vorticity distributions with non-zero circulation, the perturbation tends to the steady solution first mentioned in Michalke & Timme (1967), while for zero circulation, the perturbation grows without bound. The latter case has potentially important implications for the stability of isolated eddies in geophysics.

Numerical and analytical investigation for solutions of fractional Oskolkov–Benjamin–Bona–Mahony–Burgers equation describing propagation of long surface waves

2021 ◽  
Author(s):  
B Sagar ◽  
S. Saha Ray
Keyword(s):  
Finite Difference ◽  
Numerical Scheme ◽  
Soliton Solutions ◽  
Type Equation ◽  
Analytical Investigation ◽  
Stability And Convergence ◽  
Kudryashov Method ◽  
Collocation Approach ◽  
The Stability ◽  
Kansa Method

In this paper, a novel meshless numerical scheme to solve the time-fractional Oskolkov–Benjamin–Bona–Mahony–Burgers-type equation has been proposed. The proposed numerical scheme is based on finite difference and Kansa-radial basis function collocation approach. First, the finite difference scheme has been employed to discretize the time-fractional derivative and subsequently, the Kansa method is utilized to discretize the spatial derivatives. The stability and convergence analysis of the time-discretized numerical scheme are also elucidated in this paper. Moreover, the Kudryashov method has been utilized to acquire the soliton solutions for comparison with the numerical results. Finally, numerical simulations are performed to confirm the applicability and accuracy of the proposed scheme.

A Parallel Block Predictor-Corrector Method by Python-Based Distributed Computing

2012 ◽  
Vol 263-266 ◽  
pp. 1315-1318
Author(s):  
Kun Ming Yu ◽  
Ming Gong Lee
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Numerical Method ◽  
Initial Value Problem ◽  
Message Passing ◽  
Message Passing Interface ◽  
Parallel Structure ◽  
Initial Value ◽  
Speed Up ◽  
Predictor Corrector

This paper is to discuss how Python can be used in designing a cluster parallel computation environment in numerical solution of some block predictor-corrector method for ordinary differential equations. In the parallel process, MPI-2(message passing interface) is used as a standard of MPICH2 to communicate between CPUs. The operation of data receiving and sending are operated and controlled by mpi4py which is based on Python. Implementation of a block predictor-corrector numerical method with one and two CPUs respectively is used to test the performance of some initial value problem. Minor speed up is obtained due to small size problems and few CPUs used in the scheme, though the establishment of this scheme by Python is valuable due to very few research has been carried in this kind of parallel structure under Python.

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