scholarly journals Stability and Convergence of Variable Order Multistep Methods

1974 ◽  
Vol 11 (5) ◽  
pp. 1044-1058 ◽  
Author(s):  
C. W. Geart ◽  
D. S. Watanabe
Keyword(s):  
Multistep Methods ◽  
Stability And Convergence ◽  
Variable Order

scholarly journals Stability and Convergence of a Time-Fractional Variable Order Hantush Equation for a Deformable Aquifer

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Abdon Atangana ◽  
S. C. Oukouomi Noutchie
Keyword(s):  
Partial Derivative ◽  
Mathematical Formulation ◽  
Stability And Convergence ◽  
Order Derivative ◽  
Variable Order ◽  
Leaky Aquifer ◽  
The Stability ◽  
Nicolson Scheme ◽  
Variable Order Derivative ◽  
Modified Equation

The medium through which the groundwater moves varies in time and space. The Hantush equation describes the movement of groundwater through a leaky aquifer. To include explicitly the deformation of the leaky aquifer into the mathematical formulation, we modify the equation by replacing the partial derivative with respect to time by the time-fractional variable order derivative. The modified equation is solved numerically via the Crank-Nicolson scheme. The stability and the convergence in this case are presented in details.

scholarly journals Explicit Finite-Difference Scheme for the Numerical Solution of the Model Equation of Nonlinear Hereditary Oscillator with Variable-Order Fractional Derivatives

2016 ◽  
Vol 26 (3) ◽  
pp. 429-435 ◽  
Author(s):  
Roman I. Parovik
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Fractional Derivatives ◽  
Stability And Convergence ◽  
Variable Order ◽  
The Difference ◽  
Explicit Finite Difference ◽  
The Stability ◽  
Variable Order Fractional Derivatives

Abstract The paper deals with the model of variable-order nonlinear hereditary oscillator based on a numerical finite-difference scheme. Numerical experiments have been carried out to evaluate the stability and convergence of the difference scheme. It is argued that the approximation, stability and convergence are of the first order, while the scheme is stable and converges to the exact solution.

scholarly journals Multistep methods for coupled second order integro-differential equations: stability, convergence and error bounds

1997 ◽  
Vol 20 (1) ◽  
pp. 127-135
Author(s):  
Lucas Jódar ◽  
José Luis Marera ◽  
Gregorio Rubio
Keyword(s):  
Differential Equations ◽  
Error Bound ◽  
Error Bounds ◽  
Multistep Methods ◽  
Discretization Error ◽  
Second Order ◽  
Stability And Convergence ◽  
Convergence Properties

In this paper multistep methods for systems of coupled second order Volterra integro-differential equations are proposed. Stability and convergence properties are studied and an error bound for the discretization error is given.

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