Extension of the spectral-transform method for solving nonlinear differential difference equations

1978 ◽  
Vol 22 (17) ◽  
pp. 691-696 ◽  
Author(s):  
D. Levi ◽  
O. Ragnisco
Keyword(s):  
Difference Equations ◽  
Transform Method ◽  
Spectral Transform

Parallelizing the spectral transform method

1992 ◽  
Vol 4 (4) ◽  
pp. 269-291 ◽  
Author(s):  
Patrick H. Worley ◽  
John B. Drake
Keyword(s):  
Transform Method ◽  
Spectral Transform

scholarly journals Numerical integration of the axisymmetric Robinson-Trautman equation by a spectral method

1999 ◽  
Vol 41 (2) ◽  
pp. 271-280 ◽  
Author(s):  
D. A. Prager ◽  
A. W.-C. Lun
Keyword(s):  
Numerical Integration ◽  
Spectral Decomposition ◽  
Finite Difference Schemes ◽  
Qualitative Comparison ◽  
Transform Method ◽  
Higher Order Modes ◽  
Spectral Transform ◽  
Long Time ◽  
Bondi Mass ◽  
Meteorological Problems

AbstractWe have adapted the Spectral Transform Method, a technique commonly used in non-linear meteorological problems, to the numerical integration of the Robinson-Trautman equation. This approach eliminates difficulties due to the S2 × R+ topology of the equation. The method is highly accurate for smooth data and is numerically robust. Under spectral decomposition the long-time equilibrium state takes a particularly simple form: all nonlinear (l ≥ 2) modes tend to zero. We discuss the interaction and eventual decay of these higher order modes, as well as the evolution of the Bondi mass and other derived quantities. A qualitative comparison between the Spectral Transform Method and two finite difference schemes is given.

scholarly journals General Solution of Linear Fractional Neutral Differential Difference Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Hai Zhang ◽  
Jinde Cao ◽  
Wei Jiang
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Difference Equations ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Linear Ordinary Differential Equations ◽  
Exponential Estimates ◽  
The Laplace Transform ◽  
Gronwall Integral Inequality ◽  
Delay Differential

This paper is concerned with the general solution of linear fractional neutral differential difference equations. The exponential estimates of the solution and the variation of constant formula for linear fractional neutral differential difference equations are derived by using the Gronwall integral inequality and the Laplace transform method, respectively. The obtained results extend the corresponding ones of integer order linear ordinary differential equations and delay differential equations.

scholarly journals Solving Riccati type q-Difference Equations via Difference Transform Method

2021 ◽  
Vol 26 (4) ◽  
Author(s):  
Ayad Raisan Khudair ◽  
Ahmed Y. Abdulmajeed
Keyword(s):  
Difference Equations ◽  
Positive Constant ◽  
Time Scale ◽  
Taylor Formula ◽  
Transform Method ◽  
Quantum Calculus ◽  
The Difference ◽  
Delta Derivative

In this paper, we deal on the time scale that its delta derivative of graininess function is a nonzero positive constant. Based on the Taylor formula for this time scale, we investigate the difference transform method (DTM). This method has been applied successfully to solve Riccati type difference equations in quantum calculus. To demonstrate the ability and efficacy of this method, some examples have been provided.

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