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Solution of 2D non-homogenous wave equation by using polywave functions

Sokała M.

Computer Assisted Mechanics and Engineering Sciences

2009

Vol. 16, No. 3/4

209-221

The paper presents a specific technique of solving the non-homogenous wave equation with the use of Trefftz functions for the wave equation. The solution was presented as a sum of a general integral and a particular integral. The general integral was expressed in the form of a linear combination of Trefftz functions for the wave equation. In order to obtain the particular integral polywave functions were used. They were generated by using the inverse operator L -1 of the equation taking into consideration the Trefftz functions.

Wave polynomials in elasticity problems

Maciąg A.

Engineering Transactions

2007

Vol. 55, iss. 2

129-153

The paper demonstrates a new technique of obtaining the approximate solution of the two- and threedimensional elasticity problems. The system of equations of elasticity can be converted to the system of wave equation. In this case, as solving functions (Trefftz functions), the so-called wave polynomials can be used. The presented method is useful for a finite body of a certain shape. Then the obtained solutions are coupled through initial and boundary conditions. Recurrent formulas for the two- and three-dimensional wave polynomials and their derivatives are obtained. The methodology for solution of systems of partial differential equations with common initial and boundary conditions by means of solving functions is presented. The advantage of using the method of solving functions is that the solution exactly satisfies the given equation (or system of equations). Some examples are included.

Wave polynomials for solving different types of two-dimensional wave equations

Maciąg A., Wauer J.

Computer Assisted Mechanics and Engineering Sciences

2005

Vol. 12, No. 4

364-378

The paper demonstrates a specific power series expansion technique used to obtain the approximate solution of the two-dimensional wave equation in some unusual cases. The solution for inhomogeneous wave equation, for more complicated shape geometry of the body, discrete boundary conditions and a membrane whose thickness is not constant is shown. As solving functions (Trefftz functions), so-called wave polynomials are used. Recurrent formulas for the particular solution are obtained. Some examples are included.