Wavelet-Based Method for Solving Linear Elliptic PDE with Dirichlet Boundary Conditions on Irregular Domains | Chapter 8 | Theory and Practice of Mathematics and Computer Science Vol. 8

The Finite Difference Fictitious Domain Wavelet Method (FDFDWM) with penalty parameter is presented in this chapter of the book for solving two-dimensional linear elliptic PDEs with Dirichlet boundary conditions specified on irregular geometric domains.

Author(s) Details

Dr. Francis Ohene Boateng
Department of Mathematics Education, Akenten Appiah-Menka University of Skills Training and Entrepreneurial Development, Kumasi, Ghana

Prof. Joseph Ackora-Prah
Department of Mathematics, Kwame Nkrumah University of Science and Technology Kumasi, Ghana.

Dr. Benedict Barnes
Department of Mathematics, Kwame Nkrumah University of Science and Technology Kumasi, Ghana.

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Critical Study on Finite Element Solution of a Boundary Value Problems for Equation Gravity Gyroscopic Waves in the Time Domain | Chapter 8 | Recent Studies in Mathematics and Computer Science Vol.4

 In the present work, on the base of a numerical finite element method, the solution of the Dirichlet and

Neumann problems with respect to the oscillation equation for gravity-gyroscopic waves is discussed. The
approximation with respect to spatial variables is achieved by using linear splines, and the approximation with
respect to time is achieved by using cubic Hermitean splines. It is demonstrated that the use of such
approximation with respect to time allows the quality of the solution to be essentially improved as compared
with the traditional approximation ensuring the second order accuracy. The stability and accuracy of the method
are estimated. Using the method of regularization with spectrum shift, a new method is developed for solving
the spatial operator degeneration problem associated with the Neumann problem. The results of the numerical
calculations performed provide the possibility to make conclusions on the mode of behavior of the solution of
the Neumann problem depending on the problem variables.

Author(s) Details

Mikhail Nikolayevich Moskalkov
Berdakh Kara-Kalpak State University, Nukus, Uzbekistan.

Dauletbay Utebaev
Berdakh Kara-Kalpak State University, Nukus, Uzbekistan.

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