An Efficient Meshless Method for Solving Multi-dimensional Nonlinear Schrödinger Equation

Habibirad, Ali; Hesameddini, Esmail; Taleei, Ameneh

doi:10.1007/s40995-020-00864-w

Cited by 6 publications

(2 citation statements)

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“…Meshfree techniques 33‐41 are very interesting and impressive for solving PDEs since these methods include simple projecting, variety in solving metamorphosis, and have capability to improve non‐smooth solutions. The meshless local Petrov–Galerkin (MLPG) method is an efficient meshfree method to solve PDEs with complicated domains.…”

Section: Introductionmentioning

confidence: 99%

“…Yin et al 30 applied a class of shifted high-order numerical schemes for the fractional mobile/immobile transport equations. For other numerical methods to solving this models, see Zhao et al 31 and Wang et al 32 Meshfree techniques [33][34][35][36][37][38][39][40][41] are very interesting and impressive for solving PDEs since these methods include simple projecting, variety in solving metamorphosis, and have capability to improve non-smooth solutions. The meshless local Petrov-Galerkin (MLPG) method is an efficient meshfree method to solve PDEs with complicated domains.…”

Section: Introductionmentioning

confidence: 99%

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An efficient meshless method based on the moving Kriging interpolation for two‐dimensional variable‐order time fractional mobile/immobile advection‐diffusion model

Habibirad

Hesameddini

Heydari

et al. 2020

Math Methods in App Sciences

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In this work, we introduce an efficient meshless technique for solving the two‐dimensional variable‐order time‐fractional mobile/immobile advection‐diffusion model with Dirichlet boundary conditions. The main advantage of this scheme is to obtain a global approximation for this problem which reduces such problems to a system of algebraic equations. To approximate the first and fractional variable‐order against the time, we use the finite difference relations. The proposed method is based on the moving Kriging (MK) interpolation shape functions. To discretize this model in space variables, we use the MK interpolation. Duo to the fact that the shape functions of MK have Kronecker's delta property, boundary conditions are imposed directly and easily. To illustrate the capability of the proposed technique on regular and irregular domains, several examples are presented in different kinds of domains and with uniform and nonuniform nodes. Also, we use this scheme to simulating anomalous contaminant diffusion in underground reservoirs.

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Section: Introductionmentioning

confidence: 99%