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2018
This chapter will introduce one of the most straightforward numerical simulation methods: the finite difference method. We will show how to approximate derivatives using finite differences and discretize the equation and computational domain based on that. The discretization will be discussed for spatial and temporal derivatives sequentially.
O. A. Oleinik, V. N. Samokhin
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This chapter will introduce one of the most straightforward numerical simulation methods: the finite difference method. We will show how to approximate derivatives using finite differences and discretize the equation and computational domain based on that. The discretization will be discussed for spatial and temporal derivatives sequentially.
O. A. Oleinik, V. N. Samokhin
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1995
Finite-difference methods are important for two reasons. First, they form the background to almost all later developments. Secondly, a finite-difference method is relatively easy to construct and program to solve a particular problem, or class of problems, that may not be suitable for an existing general purpose software package using, say, finite ...
Richard L. Stoll, Kazimierz Zakrzewski
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Finite-difference methods are important for two reasons. First, they form the background to almost all later developments. Secondly, a finite-difference method is relatively easy to construct and program to solve a particular problem, or class of problems, that may not be suitable for an existing general purpose software package using, say, finite ...
Richard L. Stoll, Kazimierz Zakrzewski
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2013
Here we give a brief introduction to finite difference methods. We first explain the implicit method; then we move to the explicit method. The former is more robust, in that it converges to the solution of a partial differential equation as the discrete increments of the state variables approach zero.
L. M. Abadie, J. M. Chamorro
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Here we give a brief introduction to finite difference methods. We first explain the implicit method; then we move to the explicit method. The former is more robust, in that it converges to the solution of a partial differential equation as the discrete increments of the state variables approach zero.
L. M. Abadie, J. M. Chamorro
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2001
The finite difference method is a universally applicable numerical method for the solution of differential equations. In this chapter, for a sample parabolic partial differential equation, we introduce some difference schemes and analyze their convergence. We present the well-known Lax equivalence theorem and related theoretical results, and apply them
Kendall Atkinson, Weimin Han
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The finite difference method is a universally applicable numerical method for the solution of differential equations. In this chapter, for a sample parabolic partial differential equation, we introduce some difference schemes and analyze their convergence. We present the well-known Lax equivalence theorem and related theoretical results, and apply them
Kendall Atkinson, Weimin Han
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2001
In previous chapters, we have discussed the equations governing the structure of a steady flow and the evolution of an unsteady flow, and derived selected solutions for elementary flow configurations by analytical and simple numerical methods. To generate solutions for arbitrary flow conditions and boundary geometries, it is necessary to develop ...
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In previous chapters, we have discussed the equations governing the structure of a steady flow and the evolution of an unsteady flow, and derived selected solutions for elementary flow configurations by analytical and simple numerical methods. To generate solutions for arbitrary flow conditions and boundary geometries, it is necessary to develop ...
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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
openaire +1 more source