Improved Fourier transform methods for solving the parabolic wave equation

The Fourier Transform and the Wave Equation

We solve the Cauchy problem for the n-dimensional wave equation, where n is an odd integer, using elementary properties of the Fourier transform. We also show that the solution can be obtained by invoking Bessel functions. The wave equation has a rich history fraught with controversy, both mathematical, see [9], and physical, see [16]. It all started in 1747 when d’Alembert, in a memoir present...

Wavelet and Fourier Methods for Solving the Sideways Heat Equation

We consider an inverse heat conduction problem, the Sideways Heat Equation, which is a model of a problem, where one wants to determine the temperature on both sides of a thick wall, but where one side is inaccessible to measurements. Mathematically it is formulated as a Cauchy problem for the heat equation in a quarter plane, with data given along the line x = 1, where the solution is wanted f...

The use of iterative methods for solving Black-Scholes equation

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

Solving Theodorsen's Integral Equation for Conformal Maps with the Fast Fourier Transform and Various Nonlinear Iterative Methods

We investigate several iterative methods for the numerical solution of Theodorsen's integral equation, the discretization of which is either based on trigonometric polynomials or function families with known attenuation factors. All our methods require simultaneous evaluations of a conjugate periodic function at each step and allow us to apply the fast Fourier transform for this. In particular,...