Numerical solution for high‐order linear complex differential equations with variable coefficients

Abstract

In this paper, we have obtained the numerical solutions of complex differential equations with variable coefficients by using the Legendre Polynomials and we have performed it on two test problems. Then, we applied with different technical of error analysis to the test problems. When we compared exact solutions and numerical solutions of tables and graphs, we realized that our method is reliable, practical, and functional.

Two novel computational techniques for fractional Gardner and Cahn‐Hilliard equations

“…[27][28][29][30][31][32][33] Since most of the complex phenomena are modeled mathematically by nonlinear fractional differential equations, there are many methods in the literature to solve these equations. [27][28][29][30][31][32][33] Since most of the complex phenomena are modeled mathematically by nonlinear fractional differential equations, there are many methods in the literature to solve these equations.…”

“…The analytical and numerical solutions for the nonlinear fractional differential equations have fundamental importance. [27][28][29][30][31][32][33] Since most of the complex phenomena are modeled mathematically by nonlinear fractional differential equations, there are many methods in the literature to solve these equations. The Gardner and Cahn-Hilliard equations are studied through distinct techniques such as reduced differential transform method, 34 the modified Kudryashov technique, 35 Adomian decomposition method (ADM), 36 improved (G ′ /G) − expansion method, 37 homotopy perturbation method (HPM), 26 residual power series method (RPSM), 22 and many others.…”

New Exact Solutions for Generalized (3+1) Shallow Water-Like (SWL) Equation

“…Choosing the suitable values of parameters, we performed the numerical simulations of the obtained solutions for (16,17) case by plotting their 2D and 3D.…”

“…Lump-type solutions and their interaction solutions are generated by Sadat [5]. In this context, various papers were presented to the literature [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. The organization of this paper is as follows: firstly, we give the methodology of the improved Bernoulli sub-equation function method.…”

The Numerical Study of a Hybrid Method for Solving Telegraph Equation

“…These are differential-algebraic equations [21], partial differential equations [4, 6-8, 22, 23], and fractional differential equations [20]. Also, the other differential equation types can be solved by this hybrid method [25][26][27][28][29][30][31][32].…”