Exponential integrators for linear inhomogeneous problems

2020 ◽  
Vol 44 (1) ◽  
pp. 937-944
Author(s):  
Marina A. Medvedeva ◽  
T. E. Simos ◽  
Ch. Tsitouras
Keyword(s):  
Exponential Integrators ◽  
Inhomogeneous Problems

scholarly journals Finite energy solutions to inhomogeneous nonlinear elliptic equations with sub-natural growth terms

2020 ◽  
Vol 13 (1) ◽  
pp. 53-74 ◽  
Author(s):  
Adisak Seesanea ◽  
Igor E. Verbitsky
Keyword(s):  
Sufficient Conditions ◽  
Nonlinear Elliptic Equations ◽  
Classical Case ◽  
Finite Energy ◽  
Natural Growth ◽  
Nonlinear Elliptic ◽  
Borel Measures ◽  
Inhomogeneous Problems ◽  
Necessary And Sufficient ◽  
Quasilinear Elliptic

AbstractWe obtain necessary and sufficient conditions for the existence of a positive finite energy solution to the inhomogeneous quasilinear elliptic equation-\Delta_{p}u=\sigma u^{q}+\mu\quad\text{on }\mathbb{R}^{n}in the sub-natural growth case {0<q<p-1}, where {\Delta_{p}} ({1<p<\infty}) is the p-Laplacian, and σ, μ are positive Borel measures on {\mathbb{R}^{n}}. Uniqueness of such a solution is established as well. Similar inhomogeneous problems in the sublinear case {0<q<1} are treated for the fractional Laplace operator {(-\Delta)^{\alpha}} in place of {-\Delta_{p}}, on {\mathbb{R}^{n}} for {0<\alpha<\frac{n}{2}}, and on an arbitrary domain {\Omega\subset\mathbb{R}^{n}} with positive Green’s function in the classical case {\alpha=1}.

scholarly journals Solution of Axisymmetric Inhomogeneous Problems with the Markov Chain Monte Carlo

2019 ◽  
Vol 8 (4) ◽  
pp. 50-58 ◽  
Author(s):  
A. E. Shadare ◽  
M. N. O. Sadiku ◽  
S. M. Musa
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Data Storage ◽  
Close Agreement ◽  
Mixed Boundary ◽  
Limited Data ◽  
Numerical Techniques ◽  
Dielectric Media ◽  
Inhomogeneous Problems

With increasing complexity of EM problems, 1D and 2D axisymmetric approximations in  p, z plane are sometimes necessary to quickly solve difficult symmetric problems using limited data storage and within shortest possible time. Inhomogeneous EM problems frequently occur in cases where two or more dielectric media, separated by an interface, exist and could pose challenges in complex EM problems. Simple, fast and efficient numerical techniques are constantly desired. This paper presents the application of simple and efficient Markov Chain Monte Carlo (MCMC) to EM inhomogeneous axisymmetric Laplace’s equations. Two cases are considered based on constant and mixed boundary potentials and MCMC solutions are found to be in close agreement with the finite difference solutions.             

Exponential integrators for stiff elastodynamic problems

2014 ◽  
Vol 33 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Dominik L. Michels ◽  
Gerrit A. Sobottka ◽  
Andreas G. Weber
Keyword(s):  
Exponential Integrators

Meshfree Exponential Integrators

2013 ◽  
Vol 35 (1) ◽  
pp. A431-A452 ◽  
Author(s):  
Marco Caliari ◽  
Alexander Ostermann ◽  
Stefan Rainer
Keyword(s):  
Exponential Integrators
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