Linear multistep methods for a class of functional differential equations

1972 ◽  
Vol 19 (5) ◽  
pp. 361-372 ◽  
Author(s):  
Gene A. Kemper
Keyword(s):  
Differential Equations ◽  
Multistep Methods ◽  
Functional Differential Equations ◽  
Linear Multistep Methods ◽  
Functional Differential

scholarly journals Classical Theory of Linear Multistep Methods for Volterra Functional Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Yunfei Li ◽  
Shoufu Li
Keyword(s):  
Differential Equations ◽  
Numerical Experiments ◽  
Multistep Methods ◽  
Functional Differential Equations ◽  
Linear Multistep Methods ◽  
Interpolation Theory ◽  
Initial Value ◽  
Classical Stability ◽  
Functional Differential ◽  
Delay Differential

Based on the linear multistep methods for ordinary differential equations (ODEs) and the canonical interpolation theory that was presented by Shoufu Li who is exactly the second author of this paper, we propose the linear multistep methods for general Volterra functional differential equations (VFDEs) and build the classical stability, consistency, and convergence theories of the methods. The methods and theories presented in this paper are applicable to nonneutral, nonstiff, and nonlinear initial value problems in ODEs, Volterra delay differential equations (VDDEs), Volterra integro-differential equations (VIDEs), Volterra delay integro-differential equations (VDIDEs), etc. At last, some numerical experiments verify the correctness of our theories.

Stability of Implicit Difference Equations Generated by Parabolic Functional Differential Problems

2007 ◽  
Vol 7 (1) ◽  
pp. 68-82
Author(s):  
K. Kropielnicka
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Initial Boundary ◽  
Numerical Examples ◽  
Convergence Results ◽  
Nonlinear Parabolic ◽  
Implicit Difference Methods ◽  
Neumann Type ◽  
Difference Methods ◽  
Functional Differential

AbstractA general class of implicit difference methods for nonlinear parabolic functional differential equations with initial boundary conditions of the Neumann type is constructed. Convergence results are proved by means of consistency and stability arguments. It is assumed that given functions satisfy nonlinear estimates of Perron type with respect to functional variables. Differential equations with deviated variables and differential integral problems can be obtained from a general model by specializing given operators. The results are illustrated by numerical examples.

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