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Nonlinear Elliptic Partial Differential Equations

2017
In Chap. 5, we explained how to apply the finite element method to nonlinear ordinary differential equations. We saw that calculating the finite element solution of nonlinear differential equations required us to solve a nonlinear system of algebraic equations and discussed how these algebraic equations could be solved.
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Elliptic Partial Differential Equations

2014
International ...
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Kernel analysis of elliptic partial differential equations

IBM Systems Journal, 1966
The extrapolated Liebmann method for solving partial differential equations is selected for study. With typical computer characteristics in mind, several schemes for organizing the requisite data flow are discussed. To show the potentialities of timing formulas, as well as their limitations and the problems encountered in their construction, one of ...
E. V. Hankam, S. G. Hahn
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On nonlinear elliptic partial differential equations and hölder continuity

, 1953
1. This paper is concerned with genera! nonlinear elliptic partial differential equations of second order for functions of two independent variables. New a priori estimates for the derivatives of solutions of such equations are derived and used to obtain
L. Nirenberg
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On the cibstryctuib of discretizations of elliptic partial differential equations

Journal of Difference Equations and Applications, 1998
Algorithmic aspects of a class of finite element collocation methods for the approximate numerical solution of elliptic partial differential equations are described Locall for each finite element the approximate solution is a polynomial. polynomials corresponding toadjacent finite elements need not match continuously but their values and noumal ...
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The Computational Complexity of Elliptic Partial Differential Equations

1972
In this paper, we consider the computational complexity of the class of all procedures for computing a second order accurate approximation (on a square grid) to the solution of a linear, second order elliptic partial differential equation in a square domain.
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Weyl transforms and a degenerate elliptic partial differential equation

Proceedings of the Royal Society A, 2005
M. W. Wong
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Stable Solutions of Elliptic Partial Differential Equations

2011
Defining Stability Stability and the variations of energy Linearized stability Elementary properties of stable solutions Dynamical stability Stability outside a compact set Resolving an ambiguity The Gelfand Problem Motivation Dimension N = 1 Dimension N = 2 Dimension N => 3 Summary Extremal Solutions Weak solutions Stable weak solutions The stable ...
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Recapturing Solutions of an Elliptic Partial Differential Equation

1981
Let k 2 -C(x 2 +y 2 )≤ 0 be regular on the closure of the disk D: x 2 +y 2 2 +(k 2 - C(x 2 +y 2 )}ϕ = 0. When the restriction of ϕ to the 3D is sufficiently smooth, expansion formulae are given that recapture ϕ from its means and shifted means on an arc of the 3D. A solution is given that interpolates prescribed means at the boundary.
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Numerical solution of elliptic partial differential equation using radial basis function neural networks

Neural Networks, 2003
Jianyu Li, Siwei Luo, Yingjian Qi, Yaping Huang   +3 more
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