Results 251 to 260 of about 158,662 (296)
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1969
With the aid of electronic computers we can easily calculate the behaviour of oscillating water in even the most complex surge tank systems by using finite difference methods. Consequently these methods are of great importance.
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With the aid of electronic computers we can easily calculate the behaviour of oscillating water in even the most complex surge tank systems by using finite difference methods. Consequently these methods are of great importance.
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2016
The chapter discusses the mathematical description of transport, diffusion, and wave phenomena and their numerical simulation with finite difference methods. The accuracy of the methods is investigated via stability and consistency properties assuming the existence of regular solutions.
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The chapter discusses the mathematical description of transport, diffusion, and wave phenomena and their numerical simulation with finite difference methods. The accuracy of the methods is investigated via stability and consistency properties assuming the existence of regular solutions.
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2019
The SWE are a system of two nonlinear hyperbolic PDEs that must be numerically solved to describe the time evolution of the fluid velocity and water depth in the entire computational domain. Finite-difference methods to obtain approximate numerical solutions are described in this chapter. First, basic numerical aspects are presented. The implementation
Oscar Castro-Orgaz, Willi H. Hager
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The SWE are a system of two nonlinear hyperbolic PDEs that must be numerically solved to describe the time evolution of the fluid velocity and water depth in the entire computational domain. Finite-difference methods to obtain approximate numerical solutions are described in this chapter. First, basic numerical aspects are presented. The implementation
Oscar Castro-Orgaz, Willi H. Hager
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2018
In this chapter, we describe two numerical finite difference methods which are used for solving differential equations, e.g., the Euler method and Euler-Cromer method. The emphasis here is on algorithm errors, and an explanation of what is meant by the “order” of the error.
George Rawitscher +2 more
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In this chapter, we describe two numerical finite difference methods which are used for solving differential equations, e.g., the Euler method and Euler-Cromer method. The emphasis here is on algorithm errors, and an explanation of what is meant by the “order” of the error.
George Rawitscher +2 more
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1993
The finite difference method (FDM) is an approximate method for solving partial differential equations. It has been used to solve a wide range of problems. These include linear and non-linear, time independent and dependent problems. This method can be applied to problems with different boundary shapes, different kinds of boundary conditions, and for a
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The finite difference method (FDM) is an approximate method for solving partial differential equations. It has been used to solve a wide range of problems. These include linear and non-linear, time independent and dependent problems. This method can be applied to problems with different boundary shapes, different kinds of boundary conditions, and for a
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2020
In this chapter, we will develop FD and FDTD solvers for a sequence of PDEs of increasing complexity. We will begin with the one-dimensional (1-D) wave equation, and then we will consider Laplace's equation with two spatial dimensions, Maxwell's equations for two-dimensional (2-D) problems, and the full system of three-dimensional (3-D) Maxwell's ...
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In this chapter, we will develop FD and FDTD solvers for a sequence of PDEs of increasing complexity. We will begin with the one-dimensional (1-D) wave equation, and then we will consider Laplace's equation with two spatial dimensions, Maxwell's equations for two-dimensional (2-D) problems, and the full system of three-dimensional (3-D) Maxwell's ...
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2007
Abstract In this chapter we analyse numerical schemes of finite differences. We define the stability and consistency of a scheme and show that, for linear constant coefficient, partial differential equations, stability plus consistency of a scheme implies its convergence.
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Abstract In this chapter we analyse numerical schemes of finite differences. We define the stability and consistency of a scheme and show that, for linear constant coefficient, partial differential equations, stability plus consistency of a scheme implies its convergence.
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