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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
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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Finite-difference time-domain methods
Nature Reviews Methods Primers, 2023Fernando L Teixeira +2 more
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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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Energy stable and accurate coupling of finite element methods and finite difference methods
Journal of Computational Physics, 2022Tuan Anh Dao +2 more
exaly