Finite Difference Method.pdf
2023-05-02
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Finite Difference Methods for Ordinary and Partial Differential Equations Steady-State and Time-Dependent Problems Randall J. LeVeque University of Washington Seattle, Washington
有限差分法国外教材
节选段落一：
A finite difference method
proceeds by replacing the derivatives in the differential equations with finite difference
approximations. This gives a large but finite algebraic system of equations to be solved in
place of the differential equation, something that can be done on a computer.节选段落二：
Later
in this chapter we will consider some other BVPs, including more challenging nonlinear
equations.
2.4 A simple finite difference method
As a first example of a finite difference method for solving a differential equation, consider
the second order ODE discussed above,
u00.x/ D f .x/ for 0 < x <节选段落三：
Suppose a finite difference method for a linear BVP gives a sequence of
matrix equations of the form AhU h D F h, where h is the mesh width.
A finite difference method
proceeds by replacing the derivatives in the differential equations with finite difference
approximations. This gives a large but finite algebraic system of equations to be solved in
place of the differential equation, something that can be done on a computer.节选段落二：
Later
in this chapter we will consider some other BVPs, including more challenging nonlinear
equations.
2.4 A simple finite difference method
As a first example of a finite difference method for solving a differential equation, consider
the second order ODE discussed above,
u00.x/ D f .x/ for 0 < x <节选段落三：
Suppose a finite difference method for a linear BVP gives a sequence of
matrix equations of the form AhU h D F h, where h is the mesh width.
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