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Elementary Boundary Value Problems
American Journal of Physics, 1966The solution of a particular elementary boundary value problem is presented. A new set of orthogonal functions is needed. Their properties are discussed briefly. A comment is made about the number of independent solutions of a rth order equation in an n dimensional space. The number is rn and not r·n.
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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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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
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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
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General Boundary-Value Problems
1992Section 5.1 introduces the general elliptic linear differential equation of second order together with the Dirichlet boundary values. An important statement is the maximum-minimum principle in §5.1.2. In §5.1.3 sufficient conditions for the uniqueness of the solution and the continuous dependence on the data are proved.
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1988
When a person begins the study of ordinary differential equations, he is usually confronted first by initial value problems, i.e. a differential equation plus conditions which the solution must satisfy at a given point x = x0.
Mayer Humi, William Miller
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When a person begins the study of ordinary differential equations, he is usually confronted first by initial value problems, i.e. a differential equation plus conditions which the solution must satisfy at a given point x = x0.
Mayer Humi, William Miller
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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 ...
L. C. Piccinini +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 ...
L. C. Piccinini +2 more
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Geodetic boundary value problems I
1986Veröffentlichungen des Zentralinstituts Physik der Erde ...
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1996
Abstract The main difficulty with the nonhomogeneous Dirichlet boundary condition is related to the fact that problem (2.21) does not admit a suitable variational formulation. The standard way of handling (2.21) is based on extending the boundary data into the interior and then transforming the problem with homogeneous Dirichlet ...
P Neittaanmäki, M Rudnicki, A Savini
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Abstract The main difficulty with the nonhomogeneous Dirichlet boundary condition is related to the fact that problem (2.21) does not admit a suitable variational formulation. The standard way of handling (2.21) is based on extending the boundary data into the interior and then transforming the problem with homogeneous Dirichlet ...
P Neittaanmäki, M Rudnicki, A Savini
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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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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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