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

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.

scholarly journals A Class of Adams-like Implicit Collocation Methods of Higher Orders for the solutions of Initial Value Problems

2011 ◽  
Vol 8 (1) ◽  
pp. 47-51
Author(s):  
J. O. Fatokun ◽  
Tsaku. Nuhu ◽  
I. K. O. Ajibola
Keyword(s):  
Numerical Experiment ◽  
Initial Value Problem ◽  
Initial Value Problems ◽  
Multistep Methods ◽  
Research Work ◽  
Quadrature Rule ◽  
Collocation Methods ◽  
Initial Value ◽  
Adams Methods ◽  
Predictor Corrector

The focus of this research work is the derivation of a class of Adams-like collocation multistep methods of orders not exceeding p=9. Numerical quadrature rule is used to derive steps k= 3,...,8 of the Adams methods. Convergence of each formula derived is established in this paper. As a numerical experiment, the step six pair of the Adams method so derived was used as predictor-corrector pair to solve a non-stiff initial value problem. The absolute errors show an accuracy of o(h7).

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.

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 Oscillation Criteria of Singular Initial-Value Problem for Second Order Nonlinear Dynamic Equation on Time Scales

2018 ◽  
Vol 5 (1) ◽  
pp. 102-112 ◽  
Author(s):  
Shekhar Singh Negi ◽  
Syed Abbas ◽  
Muslim Malik
Keyword(s):  
Time Scales ◽  
Initial Value Problem ◽  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Type Inequality ◽  
Second Order ◽  
Oscillation Criterion ◽  
Initial Value ◽  
Nonlinear Dynamic Equation ◽  
Singular Initial Value Problem

AbstractBy using of generalized Opial’s type inequality on time scales, a new oscillation criterion is given for a singular initial-value problem of second-order dynamic equation on time scales. Some oscillatory results of its generalizations are also presented. Example with various time scales is given to illustrate the analytical findings.

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