Numerical approximations for space–time fractional Burgers’ equations via a new semi-analytical method

Approximation of three‐dimensional nonlinear wave equations by fundamental solutions and weighted residuals process

“…On the foundation of the main scheme devoted to mesh free methodology presented in [30] and successfully extended to various PDE problems, we take advantage of using DRM method. First, note that in every time step t l , it follows from [17,31] that, in the sense of localized particular solutions, approximations of a C l solution of Equation ( 9) will be straightforwardly obtained as Consider I a number of nodes and {x 𝑗 } I 𝑗=0 a sequence of collocation points. Using DRM method and Equation ( 9), the collocation procedure at x 𝑗 of the function ℜ l (x), (l = 0, 1, 2, … , L), simply takes the form…”

“…On the foundation of the main scheme devoted to mesh free methodology presented in [30] and successfully extended to various PDE problems, we take advantage of using DRM method. First, note that in every time step $$$ {t}_l $$$, it follows from [17, 31] that, in the sense of localized particular solutions, approximations of a $$$ {C}^l $$$ solution of Equation () will be straightforwardly obtained as $$$$ {C}^l\left(\boldsymbol{x}\right)=\sum \limits_{i=0}^I{\bar{a}}_i^l{P}_i\left(\boldsymbol{x}\right)+{C}_h^l\left(\boldsymbol{x}\right). $$$$ …”

“…As might be expected, the high applications give rise to the question of how best to solve nonlinear wave equations numerically. Several methods rely on mesh-free methodology, in which a spacious review can be found in [10,[16][17][18][19][20][21]. The MFS, boundary element (BEM), and finite element (FEM) are mainly helpful for collocation-based approximation, although the methods BEM or FEM have some deficiencies in transferring the distorted elements or re-meshing [22].…”

Solution of the Modified Time Fractional Coupled Burgers Equations Using Laplace Adomian Decompostion Method

“…Also, several other methods have been proposed to solve non-linear fractional partial differential equations. The authors [11] numerically solved space-time fractional Burgers equations with the help of a new semi-analytical method. Safari and Sun [12] solved a fractional Rayleigh-Stokes using an improved singular boundary and dual reciprocity methods.…”

Parametric quintic spline for time fractional Burger’s and coupled Burgers’ equations

“…Consider the time fractional Burger's equation (TFBE) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and the time fractional coupled Burgers' equations (TFCBEs) [18][19][20][21][22][23][24][25] defined as follows, respectively: D α t u(x, t) + u(x, t)D x u(x, t) -sD xx u(x, t) = f (x, t) for 0 < α < 1,…”