A New Efficient Method for Solving Two-Dimensional Nonlinear System of Burger’s Differential Equations

Abstract

In this work, the Sumudu decomposition method (SDM) is utilized to obtain the approximate solution of two-dimensional nonlinear system of Burger’s differential equations. This method is considered to be an effective tool in solving many problems. Our results have shown that the SDM offers a much better approximation for solving several numbers of systems of two-dimensional nonlinear Burger’s differential equations. To clarify the facility and accuracy of the strategy, two examples are provided.

A New Solution of Time-Fractional Coupled KdV Equation by Using Natural Decomposition Method

“…Theorem 5. (see [8][9][10]). If n ∈ ℕ, where n − 1 ≤ α < n and Gðs, uÞ is the natural transform of the function yðtÞ, then the natural transform of the Caputo fractional derivative ∂ ∝ yðx , tÞ/∂t ∝ is given by…”

“…Fractional partial differential equations (FPDEs) have lately been studied and solved in several ways [6,7]. Many transforms coupled with other techniques were used to solve differential equations [8][9][10]. The coupled natural transform [11][12][13][14] and Adomian decomposition method [15][16][17] called the natural decomposition method (NDM) is introduced in [18,19] to solve differential equations, and it presents the approximate solution in the series form.…”

Advantages of the Differential Equations for Solving Problems in Mathematical Physics with Symbolic Computation

“…The wave soliton pulse [6], a significant feature of nonlinearity, shows a perfect equilibrium between nonlinearity and dispersion effects. The first integral method is a powerful solution method was presented by the mathematician [7], where this method is characterized with its strength, with high accuracy and ease of application by relying on the characteristics and advantages of the differential equations as well as mathematical software in finding the exact traveling wave solutions for complex and nonlinear equations that specialized of nonlinear physical phenomena, so was applied to an important type of NLEEs and fractional equations as [8][9][10][11] with compare with other methods, for example the homotopy perturbation method [12], the generalized tanh method [13], homotopy analysis method [14], and several methods [15][16][17][18][19][20][21][22], the first integral method has proven its ability to solve various types of non-linear problems and distinguishes it from other methods by its applicable and the various solitary wave solutions that we obtain by using this method.…”

Solution of Integral Differential Equations by New Double Integral Transform (Laplace–Sumudu Transform)

“…Double integral transform and their characteristics and theories are nevertheless new and below studies [1][2][3], in which the preceding research treated some components of them along with definitions, simple theories, and the answer of normal and partial differential equations [4][5][6][7][8][9][10][11][12][13][14][15][16]; additionally, some researchers addressed these transforms and combine them with exclusive mathematical method such as differential transform approach, homotopy perturbation technique, Adomian decomposition method, and variational iteration method [7][8][9][10][11][12][13][14][15][16] so that we can solve the linear and nonlinear fractional differential equations.…”