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The purpose of this paper is to solve both eigenvalue and boundary value problems coming from the field of quantum mechanics through the application of meshless methods, particularly the one known as meshless local Petrov‐Galerkin (MLPG).

Regarding eigenvalue problems, the authors show how to apply MLPG to the time‐independent Schrödinger equation stated in three dimensions. Through a special procedure, the numerical integration of weak forms is carried out only for internal nodes. The boundary conditions are enforced through a collocation method. The final result is a generalized eigenvalue problem, which is readily solved for the energy levels. An example of boundary value problem is described by the time‐dependent nonlinear Schrödinger equation. The weak forms are again stated only for internal nodes, whereas the same collocation scheme is employed to enforce the boundary conditions. The nonlinearity is dealt with by a predictor‐corrector scheme.

Results show that the combination of MLPG and a collocation scheme works very well. The numerical results are compared to those provided by analytical solutions, exhibiting good agreement.

The flexibility of MLPG is made explicit. There are different ways to obtain the weak forms, and the boundary conditions can be enforced through a number of ways, the collocation scheme being just one of them. The shape functions used to approximate the solution can incorporate modifications that reflect some feature of the problem, like periodic boundary conditions. The value of this work resides in the fact that problems from other areas of electromagnetism can be attacked by the very same ideas herein described.

The purpose of this paper is to solve the electromagnetic scattering problem through a new integral‐based approach that uses the moving least squares (MLS) meshless method to generate its shape functions.

The electric field integral equation and its magnetic counterpart (MFIE) are discretized via special shape functions built numerically through the MLS procedure. This approach is applied to the particular problem concerning the scattering of a TM plane wave by an infinite conductor cylinder. An error norm is established in order to verify the quality of the obtained results.

Results show that the discretization process which employs MLS shape functions presents very good precision and fast convergence to the solution, when compared to results provided by another numerical method, the method of moments.

MLS shape functions occur in meshless methods intended to solve problems based on differential formulation. This paper shows that these shape functions can also be applied successfully to problems coming from an integral formulation.