Damped wave equation and dissipative wave equation in fractal strings within the local fractional variational iteration method

A Local Fractional Variational Iteration Method for Laplace Equation within Local Fractional Operators

and Applied Analysis 3 The nonlinear local fractional equation reads as L α u + N α u = 0, (19) where L α and N α are linear and nonlinear local fractional operators, respectively. Local fractional variational iteration algorithm can be written as [37] u n+1 (t) = u n (t) + t0 I t (α) {ξ α [L α u n (s) + N α u n (s)]} . (20) Here, we can construct a correction functional as follows [37]: u n+1 ...

Optimization of Solution Regularized Long-wave Equation by Using Modified Variational Iteration Method

In this paper, a regularized long-wave equation (RLWE) is solved by using the Adomian's decomposition method (ADM) , modified Adomian's decomposition method (MADM), variational iteration method (VIM), modified variational iteration method (MVIM) and homotopy analysis method (HAM). The approximate solution of this equation is calculated in the form of series which its components are computed by ...

AnEnergyConserving Local DiscontinuousGalerkin Method for a Nonlinear Variational Wave Equation

We design and numerically validate a local discontinuous Galerkin (LDG) method to compute solutions to the initial value problem for a nonlinear variational wave equation originally proposed tomodel liquid crystals. For the semi-discrete LDG formulation with a class of alternating numerical fluxes, the energy conserving property is verified. A dissipative scheme is also introduced by locally im...

The variational iteration method for solving Nagumo telegraph equation

Representation of Dissipative Solutions to a Nonlinear Variational Wave Equation

The paper introduces a new way to construct dissipative solutions to a second order variational wave equation. By a variable transformation, from the nonlinear PDE one obtains a semilinear hyperbolic system with sources. In contrast with the conservative case, here the source terms are discontinuous and the discontinuities are not always crossed transversally. Solutions to the semilinear system...