Weak formulation based Haar wavelet method for solving differential equations

Application of Higher Order Haar Wavelet Method for Solving Nonlinear Evolution Equations

“…In many numerical studies [2,12,25,41], spatial derivatives are expanded into Haar wavelet series while finite difference type schemes are used for integration with respect to time. In the present study, MATLAB's ode45 [61] solver based on Runge-Kutta (4,5) formula [17] is used for integration with respect to time.…”

“…al. in [41]. The complexity issues of strong and weak formulation based HWM are also discussed in the latter study.…”

“…In addition, the wave equation was chosen as the first model equation for its simplicity. The Burgers' equation [10,11] has previosuly been studied using the HWM [29,36,41,49] and also has an anlytical solution, thus the possibility of comparison made it a decent choice for a model equation. It finds applications in modeling of turbulence [10] and traffic [46], as well as in weak non-stationary shock wave in real fluids [31] and in nonlinear acoustics [24].…”

Numerical Solution of the One-Dimensional Heat Equation by Using Chebyshev Wavelets Method

“…From the first field of investigation the papers [8][9][10][11][12][13] can be cited. As to the elasticity problems we refer to the papers [14][15][16][17][18][19][20]. In all these papers different wavelet families have been applied.…”

A Chebyshev Wavelet Collocation Method for Some Types of Differential Problems

“…The Galerkin and collocation approaches along with wavelets [9][10][11][12] were applied in elasticity problems. For the case of the Haar wavelets, we can mention the work of Lepik et al [13].…”