DIRAC functionINITIAL value problemsIn this paper we investigate the solutions of second-order fuzzy initial value problem using the fuzzy Laplace transforms with Dirac delta function under the generalized differentiabilitiy. The related theorems and properties are given in ...
The regularity of solutions to parabolic problems with asymptotic structure of Laplacian type had already been investigated in [11], where a BMOFootnote1regularity was proved for solutions to asymptotically parabolic systems in the case\(f=0\)(see also [13], where the local Lipschitz continuity o...
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The solver is tested for initial value problems and boundary value problems of ODEs, and the results exhibit high accuracy for not only the unknown functions but also their derivatives. The same strategy can be used to construct a PDE solver based on collocation points instead of a mesh, ...
To solve first-order time-dependent problems, NDSolve needs an initial condition and a time region. Solve the PDE. In[6]:= Make an animation of the solution. In[7]:= Out[9]= Note that it is more efficient to convert the mesh once and use the discretized mesh during the plotting ...
In 2000, a non-field analytical method for solving various problems of energy and information transport has been developed by Kulish and Lage. Based on the Laplace transform technique, this elegant method yields closed-form solutions written in the form of integral equations, which relate local va...
with obtaining analytical or numerical solutions. However, researchers have made significant progress in developing novel methodologies to address this challenge. Some notable methods include the ADM [22,24,30], the Laplace transform method [16,26], the natural transform decomposition approach [37], ...
Solving a 2-D PDE system is quite similar to solving ODEs, except there are two variables x and y for boundary value problems or x and t for initial boundary value problems, both of which are supported. def pde_system(u, x, y): return [diff(u, x, order=2) + diff(u, y, order...
Finally, the resulting equations (2) may be solved in Laplace domain. The paper is organized as follows: first, Section 2 introduces the pressure diffusion model in the matrix and in the fractures considered having a small thickness ε. In Section 3.1, we summarize with more details the ...
with obtaining analytical or numerical solutions. However, researchers have made significant progress in developing novel methodologies to address this challenge. Some notable methods include the ADM [22,24,30], the Laplace transform method [16,26], the natural transform decomposition approach [37], ...