Neural network method: delay and system of delay differential equations

2021 ◽  
Author(s):  
Shagun Panghal ◽  
Manoj Kumar
Keyword(s):  
Neural Network ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Neural Network Method ◽  
Network Method ◽  
Delay Differential

scholarly journals Neural Network Method for Solving Time-Fractional Telegraph Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Wubshet Ibrahim ◽  
Lelisa Kebena Bijiga
Keyword(s):  
Neural Network ◽  
Differential Equations ◽  
Initial Boundary ◽  
Telegraph Equation ◽  
Analytic Solutions ◽  
Neural Network Method ◽  
Fractional Telegraph Equation ◽  
Network Method ◽  
Mean Square Errors ◽  
Remarkable Progress

Recently, the development of neural network method for solving differential equations has made a remarkable progress for solving fractional differential equations. In this paper, a neural network method is employed to solve time-fractional telegraph equation. The loss function containing initial/boundary conditions with adjustable parameters (weights and biases) is constructed. Also, in this paper, a time-fractional telegraph equation was formulated as an optimization problem. Numerical examples with known analytic solutions including numerical results, their graphs, weights, and biases were also discussed to confirm the accuracy of the method used. Also, the graphical and tabular results were analyzed thoroughly. The mean square errors for different choices of neurons and epochs have been presented in tables along with graphical presentations.

Sign in / Sign up

Export Citation Format

Share Document