Parametric Medial Shape Representation in 3-D via the Poisson Partial Differential Equation with Non-linear Boundary Conditions

2005 ◽  
pp. 162-173 ◽  
Author(s):  
Paul A. Yushkevich ◽  
Hui Zhang ◽  
James C. Gee
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Conditions ◽  
Shape Representation ◽  
Linear Boundary ◽  
Partial Differential ◽  
Non Linear

Cauchy's Problem in a Non-Linear Partial Differential Equation of Hyperbolic Type

1935 ◽  
Vol 31 (2) ◽  
pp. 195-202 ◽  
Author(s):  
M. Raziuddin Siddiqi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Conditions ◽  
Linear Partial Differential Equation ◽  
Positive Function ◽  
Hyperbolic Type ◽  
Partial Differential ◽  
Non Linear ◽  
Image Position

Let p (x) be an essentially positive function defined in the interval 0 ≤ x ≤ π. We consider the non-linear partial differential equationfor the boundary conditions u (x, t) = 0,for x = 0 and x = π,

scholarly journals Accuracy, Robustness, and Efficiency of the Linear Boundary Condition for the Black-Scholes Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Darae Jeong ◽  
Seungsuk Seo ◽  
Hyeongseok Hwang ◽  
Dongsun Lee ◽  
Yongho Choi ◽  
...  
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Partial Differential Equation ◽  
Boundary Conditions ◽  
Numerical Solutions ◽  
Linear Boundary ◽  
Partial Differential ◽  
Various Boundary Conditions ◽  
Linear Boundary Condition ◽  
Black Scholes

We briefly review and investigate the performance of various boundary conditions such as Dirichlet, Neumann, linear, and partial differential equation boundary conditions for the numerical solutions of the Black-Scholes partial differential equation. We use a finite difference method to numerically solve the equation. To show the efficiency of the given boundary condition, several numerical examples are presented. In numerical test, we investigate the effect of the domain sizes and compare the effect of various boundary conditions with pointwise error and root mean square error. Numerical results show that linear boundary condition is accurate and efficient among the other boundary conditions.

Nonlinear Vibrations of Non-Uniform Beams Including Inertia Effects

2005 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Ion Stroe
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Conditions ◽  
Nonlinear Vibrations ◽  
Multiple Scales ◽  
Nonlinear Partial Differential Equation ◽  
Nonlinear Effects ◽  
Order Partial Differential Equation ◽  
Partial Differential ◽  
Inertia Effects

This papers deals with nonlinear vibrations of non-uniform beams with geometrical nonlinearities such as moderately large curvatures, and inertia nonlinearities such as longitudinal and rotary inertia forces. The nonlinear fourth-order partial-differential equation describing the above nonlinear effects is presented. Using the method of multiple scales, each effect is found by reducing the nonlinear partial-differential equation of motion to two simpler linear partial-differential equations, homogeneous and nonhomogeneous. These equations along with given boundary conditions are analytically solved obtaining so-called zero-and first-order approximations of the beam’s nonlinear frequencies. Since the effect of mid-plane stretching is ignored, any boundary conditions could be considered as long as the supports are not fixed a constant distance apart. Analytical expressions showing the influence of these three nonlinearities on beam’s frequencies are presented up to some constant coefficients. These coefficients depend on the geometry of the beam. This paper can be used to study these influences on frequencies of different classes of beams. However, numerical results are presented for uniform beams. These results show that as beam slenderness increases the effect of these nonlinearities decreases. Also, they show that the most important nonlinear effect is due to moderately large curvature for slender beams.

Calculation of Elastic Induced Stress of Surrounding Rocks

2012 ◽  
Vol 170-173 ◽  
pp. 37-40
Author(s):  
Bo Qian
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Conditions ◽  
Analytical Solutions ◽  
Superposition Principle ◽  
Compatibility Conditions ◽  
Partial Differential ◽  
Induced Stress ◽  
Stress Functions ◽  
Round Section

In accordance with equilibrium differential equations and compatibility conditions of deformation, the partial differential equation of induced stress is achieved for elastic surrounding rocks of tunnels and chambers of round section. By method of the superposition principle, elastic analytical solutions of induced stress of surrounding rocks is derived from the partial differential equation, which is based on stress functions and boundary conditions.

The numerical solution of the heat conduction equation in one dimension

1964 ◽  
Vol 60 (4) ◽  
pp. 897-907 ◽  
Author(s):  
M. Wadsworth ◽  
A. Wragg
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Numerical Method ◽  
Heat Conduction Equation ◽  
Linear Equations ◽  
Conduction Equation ◽  
Partial Differential ◽  
Direct Numerical Method

AbstractThe replacement of the second space derivative by finite differences reduces the simplest form of heat conduction equation to a set of first-order ordinary differential equations. These equations can be solved analytically by utilizing the spectral resolution of the matrix formed by their coefficients. For explicit boundary conditions the solution provides a direct numerical method of solving the original partial differential equation and also gives, as limiting forms, analytical solutions which are equivalent to those obtainable by using the Laplace transform. For linear implicit boundary conditions the solution again provides a direct numerical method of solving the original partial differential equation. The procedure can also be used to give an iterative method of solving non-linear equations. Numerical examples of both the direct and iterative methods are given.

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