Two Methods to Discretize the Wave Equation in Time and Space

被引：0

作者：

Suzuki, Tomoyu ^{[1
]}

Tokutomi, Yuichi ^{[1
]}

Hori, Noriyuki ^{[1
]}

Nguyen-Van, Triet ^{[2
]}

Kawai, Shin ^{[1
]}

机构：

[1] Univ Tsukuba, Intelligent & Mech Interact Syst, 1-1-1 Tennoudai, Tsukuba, Ibaraki 3058573, Japan

[2] Oyama Coll, Natl Inst Technol, 771 Nakakuki, Oyama, Tochigi 3230806, Japan

来源：

2022 10TH INTERNATIONAL CONFERENCE ON CONTROL, MECHATRONICS AND AUTOMATION (ICCMA 2022) | 2022年

关键词：

exact-discretization-method; wave equation; digital control; variable separation; d'Alembert solution; discrete model; MODELS;

D O I：

10.1109/ICCMA56665.2022.10011619

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This study proposes two methods to derive exact discrete-time and space models for the wave equation as an example of a hyperbolic linear partial differential equation. The first method is based on the separation of variables method, an extension of the previous studies, and discretizes time and space separately. This method can accurately discretize when the initial conditions are expressed as a sum of sinusoidal functions. The second method is based on d'Alembert's method, which can be used strictly with arbitrary initial conditions, and discretizes time and space simultaneously. However, this method requires that the space be one-dimensional. Both models can be computed online, and their use is expected to have applications in control system design.

引用

页码：148 / 153

页数：6

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