The formulation and analysis of energy-preserving schemes for solving high-dimensional nonlinear Klein–Gordon equations

In this paper we focus on the analysis of energy-preserving schemes for solving high-dimensional nonlinear Klein–Gordon equations. A novel energy-preserving scheme is developed based on the discrete gradient method and the Duhamel principle. The local error, global convergence and nonlinear stability of the new scheme are analysed in detail. Numerical experiments are implemented to compare with existing numerical methods in the literature, and the numerical results show the remarkable efficiency of the new energy-preserving scheme presented in this paper.

SV-WAVE WITH EXTERNAL FORCE IN SATURATED MEDIUM

There are past researches done for SV-wave with the absence of external force. This work aims to investigate the influence of external force in the propagation of SV-wave in the soluble and insoluble mediums. Isotropic wave model is derived for SV-wave with various forces in accordance to Duhamel Principle and their analytical solutions are used to compare with each other’s’ amplitudes. With the existence of high density fluid, diffusive waves with larger external force will induce higher amplitude. However, SV-waves are non-diffusive in low density medium and hence, this work concludes that wave diffusion by external force is subjected to the properties of the targeted medium

Singular fractional evolution differential equations

We give an existence-uniqueness result for linear and nonlinear time fractional evolution equations with singularities in corresponding norm in extended Colombeau algebra of generalized functions using fractional analog for Duhamel principle. Paper deals with some nonlinear models with singularities appearing in viscoelasticity and in anomalous processes which have met great interest among researchers who consider them as a challenge in recent years.