Relevant bibliographies by topics / Dirichlet solution

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Academic literature on the topic 'Dirichlet solution'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Dirichlet solution"

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Nugraheni, Sekar, and Christiana Rini Indrati. "SOLUSI LEMAH MASALAH DIRICHLET PERSAMAAN DIFERENSIAL PARSIAL LINEAR ELIPTIK ORDER DUA." Journal of Fundamental Mathematics and Applications (JFMA) 1, no. 1 (2018): 1. http://dx.doi.org/10.14710/jfma.v1i1.2.

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The weak solution is one of solutions of the partial differential equations, that is generated from derivative of the distribution. In particular, the definition of a weak solution of the Dirichlet problem for second order linear elliptic partial differential equations is constructed by the definition and the characteristics of Sobolev spaces on Lipschitz domain in R^n. By using the Lax Milgram Theorem, Alternative Fredholm Theorem and Maximum Principle Theorem, we derived the sufficient conditions to ensure the uniqueness of the weak solution of Dirichlet problem for second order linear ellip
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Nazarova, Kulzina Zh, Batirkhan Kh Turmetov, and Kairat Id Usmanov. "On a nonlocal boundary value problem with an oblique derivative." Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva 22, no. 1 (2020): 81–93. http://dx.doi.org/10.15507/2079-6900.22.202001.81-93.

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The work studies the solvability of a nonlocal boundary value problem for the Laplace equation. The nonlocal condition is introduced using transformations in the Rn space carried out by some orthogonal matrices. Examples and properties of such matrices are given. To study the main problem, an auxiliary nonlocal Dirichlet-type problem for the Laplace equation is first solved. This problem is reduced to a vector equation whose elements are the solutions of the classical Dirichlet probem. Under certain conditions for the boundary condition coefficients, theorems on uniqueness and existence of a s
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Afrouzi, G. A. "The existence of positive solutions for an elliptic boundary value problem." International Journal of Mathematics and Mathematical Sciences 2005, no. 13 (2005): 2005–10. http://dx.doi.org/10.1155/ijmms.2005.2005.

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By using the mountain pass lemma, we study the existence of positive solutions for the equation−Δu(x)=λ(u|u|+u)(x)forx∈Ωtogether with Dirichlet boundary conditions and show that for everyλ<λ1, whereλ1is the first eigenvalue of−Δu=λuinΩwith the Dirichlet boundary conditions, the equation has a positive solution while no positive solution exists forλ≥λ1.
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Karachik, Valery. "Dirichlet and Neumann Boundary Value Problems for the Polyharmonic Equation in the Unit Ball." Mathematics 9, no. 16 (2021): 1907. http://dx.doi.org/10.3390/math9161907.

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In the previous author’s works, a representation of the solution of the Dirichlet boundary value problem for the biharmonic equation in terms of Green’s function is found, and then it is shown that this representation for a ball can be written in the form of the well-known Almansi formula with explicitly defined harmonic components. In this paper, this idea is extended to the Dirichlet boundary value problem for the polyharmonic equation, but without invoking the Green’s function. It turned out to find an explicit representation of the harmonic components of the m-harmonic function, which is a
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Grzywny, Tomasz, Moritz Kassmann, and Łukasz Leżaj. "Remarks on the Nonlocal Dirichlet Problem." Potential Analysis 54, no. 1 (2020): 119–51. http://dx.doi.org/10.1007/s11118-019-09820-9.

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AbstractWe study translation-invariant integrodifferential operators that generate Lévy processes. First, we investigate different notions of what a solution to a nonlocal Dirichlet problem is and we provide the classical representation formula for distributional solutions. Second, we study the question under which assumptions distributional solutions are twice differentiable in the classical sense. Sufficient conditions and counterexamples are provided.
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Machů, Hana. "Filippov solutions of vector Dirichlet problems." Mathematica Slovaca 70, no. 2 (2020): 401–16. http://dx.doi.org/10.1515/ms-2017-0359.

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Abstract If in the right-hand sides of given differential equations occur discontinuities in the state variables, then the natural notion of a solution is the one in the sense of Filippov. In our paper, we will consider this type of solutions for vector Dirichlet problems. The obtained theorems deal with the existence and localization of Filippov solutions, under effective growth restrictions. Two illustrative examples are supplied.
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Fašangová, Eva, and Eduard Feireisl. "The long-time behaviour of solutions to parabolic problems on unbounded intervals: the influence of boundary conditions." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 129, no. 2 (1999): 319–29. http://dx.doi.org/10.1017/s0308210500021375.

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For a non-negative function ū(x), we study the long-time behaviour of solutions of the heat equationwith the Dirichlet or Neumann boundary conditions at x = 0. We find a critical parameter λD > 0 such that the solution subjected to the Dirichlet boundary condition tends to a spatially localized wave travelling to infinity in the space variable. On the other hand, there exists a λN > 0 such that the corresponding solution of the Neumann problem converges to a non-trivial strictly positive stationary solution. Consequently, the dynamics is considerably influenced by the choice of boundary
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Algazin, O. D., and A. V. Kopaev. "A Mixed Boundary Value Problem for the Laplace Equation in a semi-infinite Layer." Mathematics and Mathematical Modeling, no. 5 (February 6, 2021): 1–12. http://dx.doi.org/10.24108/mathm.0520.0000229.

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The paper offers a solution of the mixed Dirichlet-Neumann and Dirichlet-Neumann-Robin boundary value problems for the Laplace equation in the semi-infinite layer, using the previously obtained solution of the mixed Dirichlet-Neumann boundary value problem for a layer.The functions on the right-hand sides of the boundary conditions are considered to be functions of slow growth, in particular, polynomials. The solution to boundary value problems is also sought in the class of functions of slow growth. Continuing the functions on the right-hand sides of the boundary conditions on the upper and l
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Algazin, O. D. "Polynomial Solutions of the Dirichlet Problem for the Tricomi Equation in a Strip." Mathematics and Mathematical Modeling, no. 3 (August 3, 2018): 1–12. http://dx.doi.org/10.24108/mathm.0318.0000120.

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In the paper we consider the Tricomi equation of mixed type. This equation is elliptic in the upper half-plane, hyperbolic in the lower half-plane and parabolically degenerate on the boundary of half-planes. Equations of a mixed type are used in transonic gas dynamics. The Dirichlet problem for an equation of mixed type in a mixed domain is, in general, ill- posed. Many papers has been devoted to the search for conditions for the well-posednes of the Dirichlet problem for a mixed-type equation in a mixed domain.This paper is devoted to finding exact polynomial solutions of the inhomogeneous Tr
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LaChapelle, J. "Path Integral Solution of the Dirichlet Problem." Annals of Physics 254, no. 2 (1997): 397–418. http://dx.doi.org/10.1006/aphy.1996.5650.

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Dissertations / Theses on the topic "Dirichlet solution"

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Unsurangsie, Sumalee. "Existence of a Solution for a Wave Equation and an Elliptic Dirichlet Problem." Thesis, North Texas State University, 1988. https://digital.library.unt.edu/ark:/67531/metadc331780/.

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In this paper we consider an existence of a solution for a nonlinear nonmonotone wave equation in [0,π]xR and an existence of a positive solution for a non-positone Dirichlet problem in a bounded subset of R^n.
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Neuberger, John M. (John Michael). "Existence of a Sign-Changing Solution to a Superlinear Dirichlet Problem." Thesis, University of North Texas, 1995. https://digital.library.unt.edu/ark:/67531/metadc278179/.

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We study the existence, multiplicity, and nodal structure of solutions to a superlinear elliptic boundary value problem. Under specific hypotheses on the superlinearity, we show that there exist at least three nontrivial solutions. A pair of solutions are of one sign (positive and negative respectively), and the third solution changes sign exactly once. Our technique is variational, i.e., we study the critical points of the associated action functional to find solutions. First, we define a codimension 1 submanifold of a Sobolev space . This submanifold contains all weak solutions to our proble
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Samad, Mostafa. "Approximation de la solution du problème de Dirichlet relatif... dans un domaine extérieur (Nantes, 1986)." Grenoble 2 : ANRT, 1986. http://catalogue.bnf.fr/ark:/12148/cb37601030j.

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Aibeche, Aïssa. "Quelques problèmes non linéaires dans des domaines à frontière polygonale, comportement singulier de la solution." Nice, 1985. http://www.theses.fr/1985NICE4052.

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Melin, Jaron Patric. "Examples of discontinuity for the variational solution of the minimal surface equation with Dirichlet data on a domain with a nonconvex corner and locally negative mean curvature." Thesis, Wichita State University, 2013. http://hdl.handle.net/10057/10639.

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The purpose of this thesis is to investigate the role of smoothness, specifically the smoothness of the boundary ∂Ω, in the behavior of the variational solution f on a domain Ω to the Dirichlet problem for the Minimal Surface Equation at a point O ∈ ∂Ω when the (generalized) curvature of ∂Ω has a negative upper bound in a neighborhood of O. We give examples which show that the assumption of boundary-regularity which Simon made in [12] or at least some weaker boundary-regularity assumption which excludes nonconvex corners in the boundary of the domain is necessary in order to guarantee that the
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Eschke, Andy. "Analytical solution of a linear, elliptic, inhomogeneous partial differential equation with inhomogeneous mixed Dirichlet- and Neumann-type boundary conditions for a special rotationally symmetric problem of linear elasticity." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-149965.

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The analytical solution of a given inhomogeneous boundary value problem of a linear, elliptic, inhomogeneous partial differential equation and a set of inhomogeneous mixed Dirichlet- and Neumann-type boundary conditions is derived in the present paper. In the context of elasticity theory, the problem arises for a non-conservative symmetric ansatz and an extended constitutive law shown earlier. For convenient user application, the scalar function expressed in cylindrical coordinates is primarily obtained for the general case before being expatiated on a special case of linear boundary condition
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Sargent, Ethan. "Radial Solutions to Semipositone Dirichlet Problems." Scholarship @ Claremont, 2019. https://scholarship.claremont.edu/hmc_theses/229.

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We study a Dirichlet problem, investigating existence and uniqueness for semipositone and superlinear nonlinearities. We make use of Pohozaev identities, energy arguments, and bifurcation from a simple eigenvalue.
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Kis, Ludovic. "Perturbations du problème de Dirichlet." Metz, 1998. http://docnum.univ-lorraine.fr/public/UPV-M/Theses/1998/Kis.Ludovic.SMZ9832.pdf.

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Dans toute la suite (a) sera un opérateur elliptique du second ordre, (oméga) un domaine de dimension (n), (lp) l'espace des fonctions ayant la p-ième puissance intégrable, (h) l'espace des fonctions ayant des dérivées jusqu'au premier ordre au carré intégrable, (ho) l'espace des fonctions de (h) s'annulant sur le bord, (wp) l'espace des fonctions ayant des dérivées jusqu'au deuxième ordre avec la p-ième puissance intégrable. On met entre parenthèses un symbole mathématique. Le contenu de ce travail est divisé en trois parties. Dans la première partie on étudie des équations semilinéaires de l
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Hassanpour, Mehran. "Sufficient Conditions for Uniqueness of Positive Solutions and Non Existence of Sign Changing Solutions for Elliptic Dirichlet Problems." Thesis, University of North Texas, 1995. https://digital.library.unt.edu/ark:/67531/metadc279227/.

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In this paper we study the uniqueness of positive solutions as well as the non existence of sign changing solutions for Dirichlet problems of the form $$\eqalign{\Delta u + g(\lambda,\ u) &= 0\quad\rm in\ \Omega,\cr u &= 0\quad\rm on\ \partial\Omega,}$$where $\Delta$ is the Laplace operator, $\Omega$ is a region in $\IR\sp{N}$, and $\lambda>0$ is a real parameter. For the particular function $g(\lambda,\ u)=\vert u\vert\sp{p}u+\lambda$, where $p={4\over N-2}$, and $\Omega$ is the unit ball in $\IR\sp{N}$ for $N\ge3$, we show that there are no sign changing solutions for small $\lambda$ and als
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Ali, Ismail 1961. "Uniqueness of Positive Solutions for Elliptic Dirichlet Problems." Thesis, University of North Texas, 1990. https://digital.library.unt.edu/ark:/67531/metadc330654/.

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In this paper we consider the question of uniqueness of positive solutions for Dirichlet problems of the form - Δ u(x)= g(λ,u(x)) in B, u(x) = 0 on ϑB, where A is the Laplace operator, B is the unit ball in RˆN, and A>0. We show that if g(λ,u)=uˆ(N+2)/(N-2) + λ, that is g has "critical growth", then large positive solutions are unique. We also prove uniqueness of large solutions when g(λ,u)=A f(u) with f(0) < 0, f "superlinear" and monotone. We use a number of methods from nonlinear functional analysis such as variational identities, Sturm comparison theorems and methods of order. We also p
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Books on the topic "Dirichlet solution"

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Simader, Christian G. The dirichlet problem for the Laplacian in bounded and unbounded domains: A new approach to weak, strong, and (2+k)-solutions in Sobolev-type spaces. Longman Scientific & Technical, 1996.

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Chabrowski, Jan. The Dirichlet problem with L2-boundary data for elliptic linear equations. Springer-Verlag, 1991.

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Morawiec, Grażyna. O pewnym sposobie rozwiązywania zagadnienia Dirichleta dla równań typu eliptycznego poprzez zagadnienia początkowe. Instytut Podstaw Informatyki Polskiej Akademii Nauk, 1991.

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Chabrowski, Jan. The Dirichlet problem with L²-boundary data for elliptic linear equations. Springer-Verlag, 1991.

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Molenkamp, F. Analytical solutions of dirichlet type of boundary value problem of hour-glass mode of 4-node quad. UMIST, 1999.

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Burns, Christopher. Solutions to the Dirichlet problem from complex function theory and numerical analysis. 1987.

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Book chapters on the topic "Dirichlet solution"

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Rasulov, Abdujabbor, Gulnora Raimova, and Matyokub Bakoev. "Monte Carlo Solution of Dirichlet Problem for Semi-linear Equation." In Finite Difference Methods. Theory and Applications. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11539-5_51.

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Katzourakis, Nikos. "Existence of Solution to the Dirichlet Problem via Perron’s Method." In SpringerBriefs in Mathematics. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-12829-0_5.

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Katzourakis, Nikos. "Comparison Results and Uniqueness of Solution to the Dirichlet Problem." In SpringerBriefs in Mathematics. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-12829-0_6.

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Anastassiou, George A. "Optimal Error Estimate for the Numerical Solution of Multidimensional Dirichlet Problem." In Intelligent Mathematics: Computational Analysis. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-17098-0_44.

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Gjerde, Jon. "Two classes of stochastic Dirichlet equations which admit explicit solution formulas." In Stochastic Analysis and Related Topics V. Birkhäuser Boston, 1996. http://dx.doi.org/10.1007/978-1-4612-2450-1_8.

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Praha, Dagmar Medková. "Solution of the Robin and Dirichlet Problem for the Laplace Equation." In Direct and Inverse Problems of Mathematical Physics. Springer US, 2000. http://dx.doi.org/10.1007/978-1-4757-3214-6_16.

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Chabrowski, Jan. "Cn−1-estimate of the solution of the Dirichlet problem with L2-boundary data." In The Dirichlet Problem with L2-Boundary Data for Elliptic Linear Equations. Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/bfb0095761.

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Zemskov, Serguey. "Approximate Solution of the Dirichlet Problem for Elliptic PDE and Its Error Estimate." In Computer Algebra in Scientific Computing. Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11555964_41.

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Jost, Jürgen. "The Dirichlet Principle. Variational Methods for the Solution of PDEs (Existence Techniques III)." In Partial Differential Equations. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-4809-9_10.

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Anastassiou, George A. "Optimal Estimate for the Numerical Solution of Multidimensional Dirichlet Problem for the Heat Equation." In Intelligent Mathematics: Computational Analysis. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-17098-0_45.

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Conference papers on the topic "Dirichlet solution"

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Ciric, I. R. "Formal expressions for the solution of Dirichlet and Neumann problems." In 11th International Symposium on Antenna Technology and Applied Electromagnetics [ANTEM 2005]. IEEE, 2005. http://dx.doi.org/10.1109/antem.2005.7852052.

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Rasulov, Abdujabar, Gulnora Raimova, and Matyokub Bakoev. "Solution of some semi-linear Dirichlet problem by Monte Carlo method." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0026724.

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Joshi, Sarang C., Michael I. Miller, Gary E. Christensen, Ayan Banerjee, Tom Coogan, and Ulf Grenander. "Hierarchical brain mapping via a generalized Dirichlet solution for mapping brain manifolds." In SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, edited by Robert A. Melter, Angela Y. Wu, Fred L. Bookstein, and William D. K. Green. SPIE, 1995. http://dx.doi.org/10.1117/12.216420.

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Malaspina, Angelica, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Integral Representation for the Solution of Dirichlet Problem for the Stokes System." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636766.

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Ahmad, Muhammad Jalil, and Korhan Günel. "Numerical Solution of Dirichlet Boundary Value Problems using Mesh Adaptive Direct Search Optimization." In International Students Science Congress. Izmir International Guest Student Association, 2021. http://dx.doi.org/10.52460/issc.2021.030.

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This study gives a different numerical approach for solving second order differential equation with a Dirichlet boundary condition. Mesh Adaptive Direct Search (MADS) algorithm is adopted to train the feed forward neural network used in this approach. As MADS is a derivative-free optimization algorithm, it helps us to reduce the time-consuming workload in the training stage. The results obtained from this approach are also compared with Generalized Pattern Search (GPS) algorithm.
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Maffucci, A., A. Perrotta, S. Ventre, and A. Tamburrino. "Numerical Solution of Electromagnetic Scattering Problems Based on the Dirichlet-to-Neumann Map." In 2018 IEEE 4th International Forum on Research and Technology for Society and Industry (RTSI). IEEE, 2018. http://dx.doi.org/10.1109/rtsi.2018.8548371.

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Ashyralyev, Allaberen, Okan Gercek, and Emel Zusi. "Numerical solution of a two dimensional elliptic-parabolic equation with Dirichlet-Neumann condition." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2018). Author(s), 2018. http://dx.doi.org/10.1063/1.5049040.

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Ozdemir, Yildirim, and Mecra Eser. "Numerical solution of the elliptic-Schrödinger equation with the Dirichlet and Neumann condition." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2014). AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4893868.

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Alcoforado Sphaier, Leandro, Diego Knupp, and Isabela Florindo Pinheiro. "COMPARISON OF EIGENPROBLEM SOLUTION APPROACHES FOR DIRICHLET CONDITIONS IN IRREGULAR DOMAINS VIA INTEGRAL TRANSFORMS." In 24th ABCM International Congress of Mechanical Engineering. ABCM, 2017. http://dx.doi.org/10.26678/abcm.cobem2017.cob17-1542.

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Ashyralyyev, Charyyar, and Gulzipa Akyüz. "Stability estimates for solution of Bitsadze-Samarskii type inverse elliptic problem with Dirichlet conditions." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2016). Author(s), 2016. http://dx.doi.org/10.1063/1.4959743.

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