[PDF] Top 20 The General Analytical and Numerical Solution for the Nonlinear Klein-Gordon Equation

... Where α, β andγ are known constant. In the present pa- per Bernstein polynomialsand Bernstein operational ma- trix is presented. In this approach, a truncated Bernstein series together with the Bernstein operational ... See full document

... more nonlinear equations, a one- dimensional (1D) lattice Boltzmann scheme with an amending function for the nonlinear Klein-Gordon equation is ...the nonlinear ... See full document

... a numerical scheme to approximate solutions of the nonlinear Klein-Gordon equation by applying the multiquadric quasi-interpolation scheme and the integrated radial basis function ... See full document

... a numerical model to simulate long waves, such as storm surge or tsunami, propagation and ...and nonlinear mechanics very recently, Song and Zhang [] solved the fractional KdV-Burgers-Kuramoto ... See full document

... and numerical solutions, in particular, traveling wave solutions, of nonlinear equations in mathematical physics plays an important role in nonlinear ...of nonlinear partial differential ... See full document

... and nonlinear Klein–Gordon ...time-fractional Klein–Gordon ...trial equation method had been applied to obtain the solution for some nonlinear fractional ... See full document

... some numerical research has been done in this ...the nonlinear Klein-Gordon equation for the same nonlinear term we study in this paper; one of the most important features of ... See full document

... and nonlinear phenomena appear in several areas of scientific fields like physics, chemistry and biology can be modeled by different type of partial differential equation such as evolution equation, ... See full document

... exact solution to Nonlinear Klein-Gordon equation (NK-GE) with quadratic ...exact solution to two one-dimensional NK-GE with quadratic ...series solution of those obtained ... See full document

... exact solution of the governing equation as the seperate solutions of the linear and nonlinear equations in a given sequential order [3], in which the solution of the nonlinear part is ... See full document

... to Equation (9) which can applied to Equation (7) to obtain a first-order ordinary differential ...exact solution to Equation (5) is then obtained by solving the equations that are obtained ... See full document

... nonhomogeneous Klein–Gordon– Maxwell system were got by Chen and ...of Klein–Gordon–Maxwell system with a very general nonlinear ...term. Klein–Gordon–Maxwell ... See full document

... and Nonlinear Klein-Gordon ...the solution in a rapid convergent series which results in the solution being in closed ...an analytical approximation, in many cases even an exact ... See full document

... perturbed nonlinear Klein-Gordon equation. The nonlinear Klein-Gordon equation is used to model many nonlinear ...new analytical solutions with small ... See full document

... differential equation frequently appear in variety of applications [9, 10], so lots of scientists have been focused on solving them, but unfortunately most of these equations do not have exact solutions, so for ... See full document

... (weak) solution. Then the generalized solution u ∈ G R × [0, ∞) is associated with ...continuous solution on the initial ...distributional solution, in general. Yet the solution ... See full document

... the solution. In section 3, we apply this method to some linear and nonlinear Schrodinger ...of numerical experiments are also presented in this ... See full document

... on numerical methods for solving ordinary differential ...differential equation using Euler and Runge Kutta 4 th order ...differential equation is analyzed on Euler and Runge-Kutta method to find the ... See full document

... the numerical solution of a nonlinear integro- differential equation modeling the temporal variation of the mean number density a(t) in the single-species annihilation reaction A + A → ∅ is ... See full document

... UoX,t, VoX,t be solutions of the free Klein-Gordon equations ] vo +oav o =0 respectively with initial data at time t=0 so that.. The proof is done by induction.[r] ... See full document