Department of Applied Mathematics, University of Kurdistan, Sanandaj, Iran.
10.22034/cmde.2026.71478.3592
Abstract
In this paper, we employ a collocation method based on the auto-correlation functions of Daubechies wavelet scaling functions to approximate the solutions of one-dimensional Burgers' equations. By using the properties of these wavelet bases, we approximate the Burgers’ equation at dyadic points for $x$ dimensional, effectively reducing it to a system of ordinary differential equations (ODEs). We then apply the fourth-order Runge-Kutta method to solve this system of ODEs. The numerical results obtained demonstrate the efficiency and accuracy of our approach compared to other existing methods.
Zafari, M. and AliPanah, A. (2026). COLLOCATION METHOD USING AUTO-CORRELATION FUNCTIONS OF COMPACT SUPPORTED WAVELET FOR SOLVING BURGERS' EQUATION. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2026.71478.3592
MLA
Zafari, M. , and AliPanah, A. . "COLLOCATION METHOD USING AUTO-CORRELATION FUNCTIONS OF COMPACT SUPPORTED WAVELET FOR SOLVING BURGERS' EQUATION", Computational Methods for Differential Equations, , , 2026, -. doi: 10.22034/cmde.2026.71478.3592
HARVARD
Zafari, M., AliPanah, A. (2026). 'COLLOCATION METHOD USING AUTO-CORRELATION FUNCTIONS OF COMPACT SUPPORTED WAVELET FOR SOLVING BURGERS' EQUATION', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2026.71478.3592
CHICAGO
M. Zafari and A. AliPanah, "COLLOCATION METHOD USING AUTO-CORRELATION FUNCTIONS OF COMPACT SUPPORTED WAVELET FOR SOLVING BURGERS' EQUATION," Computational Methods for Differential Equations, (2026): -, doi: 10.22034/cmde.2026.71478.3592
VANCOUVER
Zafari, M., AliPanah, A. COLLOCATION METHOD USING AUTO-CORRELATION FUNCTIONS OF COMPACT SUPPORTED WAVELET FOR SOLVING BURGERS' EQUATION. Computational Methods for Differential Equations, 2026; (): -. doi: 10.22034/cmde.2026.71478.3592
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