Haar wavelet approach to nonlinear stiff systems

Hsiao, C. H.; Wang, Wen-June

doi:10.1016/s0378-4754(01)00275-0

Cited by 114 publications

(29 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Stability was guaranteed in the case of implicit methods (in [7] the Runge-Kutta codes DOPRI 5 and RADAU 5 were applied). In [11] the system (5.1) is integrated by the single term Haar wavelet method and in [14] the Adomian decomposition method was used. Solution obtained by the ODE45 code is plotted in Fig.…”

Section: Nonlinear Problemsmentioning

confidence: 99%

See 1 more Smart Citation

Haar Wavelet Method for Solving Stiff Differential Equations

Lepik

2009

Mathematical Modelling and Analysis

View full text Add to dashboard Cite

show abstract

Section: Nonlinear Problemsmentioning

confidence: 99%

“…Hsiao [9,10,11] has proposed for solving linear and nonlinear differential equations the so called single-term Haar wavelet method (in fact it is a method of piecewise constant approximation). The method is very simple and effective, but its exactness in the region of rapid changes may turn out to be insufficient (see, Fig.…”

Section: Introductionmentioning

confidence: 99%

Haar Wavelet Method for Solving Stiff Differential Equations

Lepik

2009

Mathematical Modelling and Analysis

View full text Add to dashboard Cite

show abstract

“…Then integrate this approximation to get the lower order derivatives in the equation. Many authors use this technique to solve the differential and integral equations [16,17,18,19,20].…”

Section: Introductionmentioning

confidence: 99%

Memory Effects Due to Fractional Time Derivative and Integral Space in Diffusion Like Equation Via Haar Wavelets

Youssef¹

2016

ACM

View full text Add to dashboard Cite

Abstract:Memory and hereditary effects due to fractional time derivative are combined with the global behaviours due to space integral term. Haar wavelet operational matrix is adjusted to solve diffusion like equations with time fractional derivative, space derivatives and integral terms. The fractional derivative is understood in the Caputo sense. The memory behaviours is included in all the points of the domain due to the existence of space integral term and the inverse fractional operator treatment and this is ilustrated in error graphs introduced. A general example with four subproblems ranging from the simple classical heat equation to the fractional time diffusion equation with global integral term is proposed and the calculated results are displayed graphically.

show abstract

“…Carroll presents an exponential fitted scheme for solving stiff systems of initial value problems [3]. The numerical solution of linear and nonlinear system of stiff system can be found in [4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Exact Solution for a Class of Stiff Systems by Differential Transform Method

Idrees¹,

Mabood²,

Ali³

et al. 2013

View full text Add to dashboard Cite

In this paper, Differential Transform Method (DTM) is proposed for the closed form solution of linear and non-linear stiff systems. First, we apply DTM to find the series solution which can be easily converted into exact solution. The method is described and illustrated with different examples and figures are plotted accordingly. The obtained result confirm that DTM is very easy, effective and convenient.

show abstract

Haar wavelet approach to nonlinear stiff systems

Cited by 114 publications

References 13 publications

Haar Wavelet Method for Solving Stiff Differential Equations

Haar Wavelet Method for Solving Stiff Differential Equations

Memory Effects Due to Fractional Time Derivative and Integral Space in Diffusion Like Equation Via Haar Wavelets

Exact Solution for a Class of Stiff Systems by Differential Transform Method

Contact Info

Product

Resources

About