method of fundamental solutionsmethod of particular solutionserror analysisstability analysisThe Cauchy problems of Laplace's equation are ill-posed with severe instability. In this paper, numerical solutions are solicited by the method of fundamental solutions (MFS) and the method of particular solutions...
Implicit solutions can also be devised. Recall from equation (2.45) that we have a linear relation among the values of u(xk) and the neighbors involved in the derivatives. Actually, if equation (2.45) is extended to all the points within domain Ω, we get a linear system that we write ...
摘要: Using a spreadsheet routine on a personal computer, we obtain solutions to Laplace's equation quickly, even with dielectricinterfaces present. This provides an alternative to solving electrostatics problems normally dealt with by relaxation methods in fortran programs or Fourier seriessolutions....
The existence and uniqueness of weak solutions are studied to the initial Dirichlet problem of the equationut=div(|u|p(x)2u)+f(x,t,u), with infp(x)>2. The problems describe the motion of generalized Newtonian fluids which were studied by some other authors in which the exponent p was...
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Laplace EquationIn this paper a Cauchy problem for a two-dimensional Laplace equation under the condition that an exact solution belongs to a compact set is considered. We solve this problem as an operator equation. The errors of the operator and the right-hand side are found under a ...
+ ∂ 2 u ∂z 2 =0.(24.3) •Noinitialconditionsrequired. •Onlyboundaryconditions. TheLaplacianinPolarCoordinates:∆u= ∂ 2 u ∂r 2 + 1 r ∂u ∂r + 1 r 2 ∂ 2 u ∂θ 2 =0. 24.3Laplace’sEquationintwodimensions PhysicalproblemsinwhichLaplace’sequationarises •...
Numerical solutions for the two-dimensional Laplace equation using isosceles right triangular cell-centred and square control volumes are compared in this work. The methodology employed for the square grids is the one related to unstructured grids, while for the square volumes the discretization process...
solutions is proposed for the numerical solution of some inverse boundary value problems associated with the Helmholtz equation, including the Cauchy problem. ... Bangti,Jin,and,... - 《International Journal for Numerical Methods in Engineering》 被引量: 244发表: 2006年 Large time behavior of th...
The moment approach to solve the Cauchy problems is investigated. First, we consider the Cauchy problem for the Laplace equation, and we present a moment method for solving it in the case of a flat boundary. Second, we consider the reciprocity gap concept used to solve the problem of crack...