Approximate Solutions of Initial Value Problems for Ordinary Differential Equations Using Radial Basis Function Networks

2017 ◽  
Vol 48 (2) ◽  
pp. 1063-1071 ◽  
Author(s):  
Fatma B. Rizaner ◽  
Ahmet Rizaner
Keyword(s):  
Differential Equations ◽  
Radial Basis Function ◽  
Ordinary Differential Equations ◽  
Basis Function ◽  
Initial Value Problems ◽  
Approximate Solutions ◽  
Radial Basis Function Networks ◽  
Initial Value ◽  
Radial Basis

Cosine Radial Basis Function Neural Networks for Solving Fractional Differential Equations

2017 ◽  
Vol 9 (3) ◽  
pp. 667-679 ◽  
Author(s):  
Haidong Qu
Keyword(s):  
Neural Networks ◽  
Differential Equations ◽  
Radial Basis Function ◽  
Fractional Differential Equations ◽  
Basis Function ◽  
Numerical Solutions ◽  
Langevin Equations ◽  
Initial Value ◽  
Radial Basis ◽  
Fractional Differential

AbstractIn this paper, we first apply cosine radial basis function neural networks to solve the fractional differential equations with initial value problems or boundary value problems. In the examples, we successfully obtained the numerical solutions for the fractional Riccati equations and fractional Langevin equations. The computer graphics and numerical solutions show that this method is very effective.

scholarly journals Optimization of one-step hybrid method for direct solution of fifth order ordinary differential equations of initial value problems

2021 ◽  
Vol 9 (1) ◽  
pp. 239-249
Author(s):  
Roseline Bosede Ogunrinde ◽  
Ololade Funmilayo Fayose ◽  
Taiwo Stephen Fayose
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Hybrid Method ◽  
Basis Function ◽  
Initial Value Problems ◽  
Test Problems ◽  
Direct Solution ◽  
Initial Value ◽  
Unknown Parameters ◽  
Fifth Order

This paper focuses on the derivation, analysis and implementation of a hybrid method by optimizing the order of the method by introduction of six-hybrid points for direct solution of fifth order ordinary differential equations of initial value problems (IVPs). Power series was used as the basis function for the solution of the IVP. The basis function was interpolated at some selected hybrid points whereas the fifth derivative of the approximate solution was collocated at all the interval of integration of the method to generate a system of linear equations for the determination of the unknown parameters. The derived method was tested for consistency, zero stability, convergence and absolute stability. The method was tested with two linear test problems to confirm its accuracy and usability. The comparison of the results with some existing methods shows the superiority of the accuracy of the method.

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