In applied sciences and engineering, partial differential equations (PDE) of integer non-integer order play a crucial role. It can be challenging to determine these equations’ exact solutions. As result, developing numerical approaches obtain precise solutions kinds takes time. The homotopy perturbation transform method (HPTM) Yang decomposition (YTDM) are the subjects several recent findings t...

we introduce a rbfs mesheless method of lines that decomposes the interior and boundary centers to obtain the numerical solution of the time dependent pdes. then, the method is applied with an adaptive algorithm to obtain the numerical solution of one dimensional problem. we show that in the problems in which the solutions contain region with rapid variation, the adaptive rbfs methods are succe...

Gaussian curvature is an important geometric property of surfaces, which has been used broadly in mathematical modeling. Due to the full nonlinearity curvature, efficient numerical methods for models based on it are uncommon literature. In this article, we propose operator-splitting method a general model. our method, decouple from differential operators by introducing two matrix- and vector-va...

We study a model of vehicular traffic flow represented by a coupled system formed by a scalar conservation law, describing the evolution of cars density, and an ODE, whose solution is the position of a moving bottleneck, i.e. a slower vehicle moving inside the cars flow. A fractional step approach is used to approximate the coupled model and convergence is proved by compactness arguments. Final...