Exponential integrator

Differential algebraic equation

Mathematics

Economic growth

Stochastic partial differential equation

Partial differential equation

Separable partial differential equation

Mathematical optimization

Mathematical analysis

Delay differential equation

Artificial intelligence

Economics

Convergence (economics)

Method of characteristics

Computer science

Differential equation

Applied mathematics

Numerical partial differential equations

Artificial neural network

Ordinary differential equation

First-order partial differential equation

Engineering With Computers

Current work introduces a fast converging neural network-based approach for solution of ordinary and partial differential equations. Proposed technique eliminates the need of time-consuming optimization procedure for training of neural network. Rather, it uses the extreme learning machine algorithm for calculating the neural network parameters so as to make it satisfy the differential equation and associated boundary conditions. Various ordinary and partial differential equations are treated using this technique, and accuracy and convergence aspects of the procedure are discussed.

Optimization free neural network approach for solving ordinary and partial differential equations