Three-dimensional Einstein-Klein-Gordon system in characteristic numerical relativity

Einstein structures on four-dimensional nutral Lie groups

When Einstein was thinking about the theory of general relativity based on the elimination of especial relativity constraints (especially the geometric relationship of space and time), he understood the first limitation of especial relativity is ignoring changes over time. Because in especial relativity, only the curvature of the space was considered. Therefore, tensor calculations should be to...

Modeling Collisionless Matter in General Relativity: A New Numerical Technique

We propose a new numerical technique for following the evolution of a self-gravitating collisionless system in general relativity. Matter is modeled as a scalar field obeying the coupled Klein-Gordon and Einstein equations. A phase space distribution function, constructed using covariant coherent states, obeys the relativistic Vlasov equation provided the de Broglie wavelength for the field is ...

Numerical solution of Klein-Gordon equation by using the Adomian's decomposition and variational iterative methods

B-SPLINE COLLOCATION APPROACH FOR SOLUTION OF KLEIN-GORDON EQUATION

We develope a numerical method based on B-spline collocation method to solve linear Klein-Gordon equation. The proposed scheme is unconditionally stable. The results of numerical experiments have been compared with the exact solution to show the efficiency of the method computationally. Easy and economical implementation is the strength of this approach.  

Analytical solutions for the fractional Klein-Gordon equation

In this paper, we solve a inhomogeneous fractional Klein-Gordon equation by the method of separating variables. We apply the method for three boundary conditions, contain Dirichlet, Neumann, and Robin boundary conditions, and solve some examples to illustrate the effectiveness of the method.