Results 341 to 350 of about 1,729,322 (384)

Differential Equations: Partial

2000
We have been studying nonlinear oscillatory processes, starting with the simplest autonomous case, and later incorporating forcing. The modelling was in terms of ordinary differential equations (ODE), and the most important tool used was the phase diagram.
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Partial Differential Equations

1988
In this chapter, procedures will be developed for classifying partial differential equations as elliptic, parabolic or hyperbolic. The different types of partial differential equations will be examined from both a mathematical and a physical viewpoint to indicate their key features and the flow categories for which they occur.
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Finite Difference Schemes and Partial Differential Equations

, 1989
Preface to the second edition Preface to the first edition 1. Hyperbolic partial differential equations 2. Analysis of finite difference Schemes 3. Order of accuracy of finite difference schemes 4. Stability for multistep schemes 5.
J. Strikwerda
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Partial Differential Equations

1978
As an example to show how the Laplace transform may be applied to the solution of partial differential equations, we consider the diffusion of heat in an isotropic solid body.
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Partial Differential Equations

2012
In this chapter we study some classes of partial differential equations, including the heat equation, the Laplace equation, and the wave equation. In particular, based on the study of Fourier series, we find solutions for several equations and several types of boundary conditions. We mainly use the method of separation of variables. In contrast to what
Luis Barreira, Claudia Valls
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Applications to Partial Differential Equations

1971
Publisher Summary The applications of integral equations are not restricted to ordinary differential equations. The most important applications of integral equations arise in finding the solutions of boundary value problems in the theory of partial differential equations of the second order.
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Optimal Control of Partial Differential Equations

Applied Mathematical Sciences, 2021
A. Manzoni, A. Quarteroni, S. Salsa
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Linear Partial Differential Equations

1957
Although we shall mainly be concerned in this Part with differential equations, the methods we use here for their discussion and solution are intimately connected with the geometry of the rest of the volume. In particular, the results obtained depend to a great extent on the theory of modules and the intersections of a set of algebraic varieties ...
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Partial Differential Equations [PDF]

, 2001
Many physical problems involve quantities that depend on more than one variable. The temperature within a “large”1 solid body of conducting material varies with both time and location within the material. When such problems are modeled, what results is a differential equation involving partial derivatives, or a partial differential equation..
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Partial Differential Equations II

2002
Partial differential equations of the form $$k{\partial \over {\partial t}}u(r,t) = \nabla ^2 u(r,t)$$ (diffusion equation) and $${{\partial ^2 } \over {\partial t^2 }}u(r,t) = c^2 \nabla ^2 u(r,t)$$ (wave equation) are amenable to the use of the Laplace transform.1 Indeed, on taking the Laplace transform of the former, we get ...
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