An approximation to the solution of hyperbolic equations by Adomian decomposition method and comparison with characteristics method

A modified spectral method for solving operator equations

“…Some method developed for solving the operator equations are analytical or semianalytical such as Adomian decomposition method [13,[16][17][18][19][20][21], homotopy analysis and homotopy perturbation methods [29][30][31][32][33][34][35][36][37][38] and variational iteration method [14,[22][23][24][25][26][27][28]. The spectral method is a famous method so we would like to modify the spectral method such that the modified one hasn't some shortcomings of spectral method.…”

Analytical Solution of Second-Order Hyperbolic Telegraph Equation by Variational Iteration and Homotopy Perturbation Methods

“…Partial differential equations are often very complicated to be solved exactly and even if an exact solution is obtainable, the required calculations may be too complicated to be practical, or it might be difficult to interpret the outcome. Recently, some promising approximate analytical solutions are proposed, such as Exp-function method [4,5], Adomian decomposition method (ADM) [6][7][8][9][10], variational iteration method (VIM) [11][12][13][14][15][16][17] and homotopy perturbation method (HPM) [18][19][20][21][22]25]. Other methods are reviewed in Refs.…”

A New Numerical Method of Estimates of Temperatures along a Thick Steel Slab and Concentrations of Alcohol along a Hollow Tube

“…Considering only the effects of molecular diffusion, determine the concentration of alcohol as a function of time and distance measured from the top of the tube. /sec at 30°c, and the vapor pressure is such that 10 volume percent alcohol in air is present at the surface [7]. The initial condition is c(x,0)=3.0 and the boundary conditions are given by c(0,t)=0, c(25,t)=15.…”