The Modified Helmholtz Equation on a Regular Hexagon—The Symmetric Dirichlet Problem
نویسندگان
چکیده
منابع مشابه
The Dirichlet Problem for the Generalized Bi-axially Symmetric Helmholtz Equation
Abstract. In [18], fundamental solutions for the generalized bi-axially symmetric Helmholtz equation were constructed in R 2 = {(x, y) : x > 0, y > 0} . They contain Kummer’s confluent hypergeometric functions in three variables. In this paper, using one of the constructed fundamental solutions, the Dirichlet problem is solved in the domain Ω ⊂ R 2 . Using the method of Green’s functions, solut...
متن کاملA Spectral Regularization Method for a Cauchy Problem of the Modified Helmholtz Equation
The Cauchy problem for Helmholtz equation arises from inverse scattering problems. Specific backgrounds can be seen in the existing literature; we can refer to 1–6 and so forth. A number of numerical methods for stabilizing this problem are developed. Several boundary element methods combined with iterative, conjugate gradient, Tikhonov regularization, and singular value decomposition methods a...
متن کاملFast integral equation methods for the modified Helmholtz equation
Talk Abstract We present an efficient integral equation method approach to solve the forced heat equation, ut(x) − ∆u(x) = F (x, u, t), in a two dimensional, multiply connected domain, with Dirichlet boundary conditions. We first discretize in time, which is known as Rothe’s method, resulting in a non-homogeneous modified Helmholtz equation that is solved at each time step. We formulate the sol...
متن کاملOn the Dirichlet problem for a Duffing type equation
Recently the classical variational problem for a Duffing type equation received again some attention. In [1], [2], [7], some variational approaches were used in order to receive the existence of solutions for both periodic and Dirichlet type boundary value problems. Mainly direct method is applied under various conditions pertaining to at most quadratic growth imposed on the nonlinear term give...
متن کاملA New Method for Solving the Modified Helmholtz Equation
In this paper, the Cauchy problem for the modified Helmholtz equation is investigated. It is known that such problem is severely ill-posed. We propose a new regularization method to solve it based on the solution given by the method of separation of variables. Error estimation and convergence analysis have been given. Finally, we present numerical results for several examples and show the effec...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Axioms
سال: 2020
ISSN: 2075-1680
DOI: 10.3390/axioms9030089