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Ozgur YILDIRIM, Burcu GÖNÜL
ON THE ANALYTICAL AND NUMERICAL SOLUTION OF THE TWO DIMENSIONAL HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS
 
In the present study we consider the analytical and numerical solution methods for the multidimensional in particular two dimesional hyperbolic partial differential equations. In modelling of the partial diffential equations hyperbolic equations model the transport of some physical quantity, such as fluids or waves. The wave equation arises in problems obtained by modelling of many natural phenomena such as vibrations, electrostatics, gas dynamics, acoustics, etc. We use Fourier series and Fourier transform methods for the solution of two dimensional hyperbolic partial differential equations. The Fourier Series is trigonometric series which allows us to model any arbitrary periodic signal with a combination of trigonometric functions sines and cosines. The Fourier Transform method is a tool that breaks a waveform into an alternate representation characterized by sine and cosines. The Fourier Transform shows that any waveform can be rewritten as the sum of sinusoidal functions. We use finite difference method to solve the two dimensional hyperbolic partial differential problem numarically. Finite difference methods are numerical methods for approximating the solutions to differential equations using finite difference equations to approximate derivatives. Some numerical experiments are illustrated. The computations are carried out by MATLAB programming and results of numerical experiments are presented in a table.

Anahtar Kelimeler: Hyperbolic differential equations, Fourier series, Fourier transform, Difference equations



 


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