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2020•Unpublished venueRequires access

PARTIAL DIFFERENTIAL EQUATIONS

Won Young Yang, Wenwu Cao, Jae-Kwon Kim, Kyung W. Park, Ho‐Hyun Park, Jingon Joung, Jong‐Suk Ro, Heekwon Lee, Cheol-Ho Hong, Taeho Im

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Abstract

This chapter considers a general second-order partial differential equation (PDE) in two independent variables, subject to the boundary conditions. These PDEs are classified into three groups: elliptic, parabolic, and hyperbolic. These three types of PDE are associated with equilibrium states, diffusion states, and oscillating system, respectively. The chapter focuses on some numerical methods for solving these PDEs, including finite element method (FEM). The FEM is procedure used in finding approximate numerical solutions to PDEs. It can handle irregular boundaries in the same way as regular boundaries. The chapter addresses what problems can be solved by using the graphical user interface tool of MATLAB for PDEs and then applies the tool to solve the elliptic/parabolic/hyperbolic equations.

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What this paper is about

This chapter considers a general second-order partial differential equation (PDE) in two independent variables, subject to the boundary conditions. These PDEs are classified into three groups: elliptic, parabolic, and hyperbolic. These three types of PDE are associated with equilibrium states, diffusion states, and oscillating system, respectively. The chapter focuses on some numerical methods for solving these PDEs, including finite element method (FEM). The FEM is procedure used in finding approximate numerical solutions to PDEs. It can handle irregular boundaries in the same way as regular boundaries. The chapter addresses what problems can be solved by using the graphical user interface tool of MATLAB for PDEs and then applies the tool to solve the elliptic/parabolic/hyperbolic equations.

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OpenAlex reports 24 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This chapter considers a general second-order partial differential equation (PDE) in two independent variables, subject to the boundary conditions. These PDEs are classified into three groups: elliptic, parabolic, and hyperbolic. These three types of PDE are associated with equilibrium states, diffusion states, and oscillating system, respectively. The chapter focuses on some numerical methods for solving these PDEs, including finite element method (FEM). The FEM is procedure used in finding approximate numerical solutions to PDEs. It can handle irregular boundaries in the same way as regular boundaries. The chapter addresses what problems can be solved by using the graphical user interface tool of MATLAB for PDEs and then applies the tool to solve the elliptic/parabolic/hyperbolic equations.

Key concepts: Partial differential equation, Elliptic partial differential equation, Mathematics, Hyperbolic partial differential equation, Finite element method, Parabolic partial differential equation, Finite volume method for one-dimensional steady state diffusion, Boundary value problem

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