The method of finite differences for nonlinear functional differential equations of the first order

2020 ◽  
Vol 27 (4) ◽  
pp. 605-616
Author(s):  
Elżbieta Puźniakowska-Gałuch
Keyword(s):  
Weak Convergence ◽  
Differential Equations ◽  
Finite Differences ◽  
Initial Conditions ◽  
Functional Differential Equations ◽  
Successive Approximations ◽  
Duality Principle ◽  
Nonlinear Functional ◽  
First Order ◽  
Functional Differential

AbstractNonlinear functional partial differential equations with initial conditions are considered on the cone. The weak convergence of a sequence of successive approximations is proved. The proof is given by the duality principle.

First Order Partial Functional Differential Equations with Unbounded Delay

2003 ◽  
Vol 10 (3) ◽  
pp. 509-530
Author(s):  
Z. Kamont ◽  
S. Kozieł
Keyword(s):  
Differential Equations ◽  
Integral Functional ◽  
Functional Differential Equations ◽  
Generalized Solutions ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
First Order ◽  
Unbounded Delay ◽  
The Cauchy Problem ◽  
Functional Differential

Abstract The phase space for nonlinear hyperbolic functional differential equations with unbounded delay is constructed. The set of axioms for generalized solutions of initial problems is presented. A theorem on the existence and continuous dependence upon initial data is given. The Cauchy problem is transformed into a system of integral functional equations. The existence of solutions of this system is proved by the method of successive approximations and by using theorems on integral inequalities. Examples of phase spaces are given.

scholarly journals Heun Method Using to Solve System of NonLinear Functional Differential Equations

2007 ◽  
Vol 4 (4) ◽  
pp. 666-669
Author(s):  
Baghdad Science Journal
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Numerical Solution ◽  
Functional Differential Equation ◽  
Functional Differential Equations ◽  
Nonlinear Functional ◽  
Numerical Examples ◽  
Nonlinear Functional Differential Equation ◽  
First Order ◽  
Functional Differential

In this paper Heun method has been used to find numerical solution for first order nonlinear functional differential equation. Moreover, this method has been modified in order to treat system of nonlinear functional differential equations .two numerical examples are given for conciliated the results of this method.

Sign in / Sign up

Export Citation Format

Share Document