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1996
Publisher Summary This chapter illustrates that the potential inside a domain of solution is specified by its boundary values at the surfaces of this domain and by its source distribution. This may be multiply connected but it always contains the optic axis.
Peter Hawkes, Erwin Kasper
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Publisher Summary This chapter illustrates that the potential inside a domain of solution is specified by its boundary values at the surfaces of this domain and by its source distribution. This may be multiply connected but it always contains the optic axis.
Peter Hawkes, Erwin Kasper
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2011
This chapter deals with Newton methods for boundary value problems (BVPs) in nonlinear partial differential equations (PDEs). There are two principal approaches: (a) finite dimensional Newton methods applied to given systems of already discretized PDEs, also called discrete Newton methods, and (b) function space oriented inexact Newton methods directly
Peter Deuflhard, Peter Deuflhard
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This chapter deals with Newton methods for boundary value problems (BVPs) in nonlinear partial differential equations (PDEs). There are two principal approaches: (a) finite dimensional Newton methods applied to given systems of already discretized PDEs, also called discrete Newton methods, and (b) function space oriented inexact Newton methods directly
Peter Deuflhard, Peter Deuflhard
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On a boundary value problem [PDF]
ANNALI DELL UNIVERSITA DI FERRARA, 1996 In this note we give an existence result for a boundary value problem for integro-differential equations.
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1984
In the previous chapters, we studied various kinds of questions concerning the initial value problem. We now propose to investigate other types of problems, in which the desired solution depends either on the values that it assumes at various points in its domain or on geometrical conditions (e.g., intersecting two given curves or being tangent to two ...
Guido Stampacchia +2 more
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In the previous chapters, we studied various kinds of questions concerning the initial value problem. We now propose to investigate other types of problems, in which the desired solution depends either on the values that it assumes at various points in its domain or on geometrical conditions (e.g., intersecting two given curves or being tangent to two ...
Guido Stampacchia +2 more
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2012
When solving initial value problems for ordinary differential equations, differential algebraic equations or partial differential equations, as discussed in previous chapters, a unique solution to the equations, if it exists, is obtained by specifying the values of all the components at the starting point of the range of integration.
G.R. Lindfield, J.E.T. Penny
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When solving initial value problems for ordinary differential equations, differential algebraic equations or partial differential equations, as discussed in previous chapters, a unique solution to the equations, if it exists, is obtained by specifying the values of all the components at the starting point of the range of integration.
G.R. Lindfield, J.E.T. Penny
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1992
The simplest frictionless contact problem of the class defined by equations (29.3–29.6) is that in which the contact area A is the circle 0 < r < a and the indenter is axisymmetric, in which case we have to determine a harmonic function φ(r, z) to satisfy the mixed boundary conditions $$\frac{{\partial \varphi }}{{\partial z}} = - \frac{\mu }{{(1 -
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The simplest frictionless contact problem of the class defined by equations (29.3–29.6) is that in which the contact area A is the circle 0 < r < a and the indenter is axisymmetric, in which case we have to determine a harmonic function φ(r, z) to satisfy the mixed boundary conditions $$\frac{{\partial \varphi }}{{\partial z}} = - \frac{\mu }{{(1 -
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2000
Linear partial differential equations the wave equation Green's function and Sturm-Liouville problems Fourier series and Fourier transforms the heat equation Laplace's equation and Poisson's equation problems in higher dimensions.
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Linear partial differential equations the wave equation Green's function and Sturm-Liouville problems Fourier series and Fourier transforms the heat equation Laplace's equation and Poisson's equation problems in higher dimensions.
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, 1971 In this section, we discuss two point boundary value problems for the nonhomogeneous equation (32.2) and obtain results of the “Fredholm alternative” type. With these results, applications to weakly nonlinear problems can be obtained in the standard, manner.
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2017
This chapter is devoted to boundary value problems for ordinary differential equations. It begins with analysis of the existence and uniqueness of solutions to these problems, and the effect of perturbations to the problem. The first numerical approach is the shooting method. This is followed by finite differences and collocation. Finite elements allow
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This chapter is devoted to boundary value problems for ordinary differential equations. It begins with analysis of the existence and uniqueness of solutions to these problems, and the effect of perturbations to the problem. The first numerical approach is the shooting method. This is followed by finite differences and collocation. Finite elements allow
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Applications to Boundary Value Problems
1989We now use results from the preceding chapters to solve the following generalization of the Dirichlet problem stated in the introduction.
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