# L11_PDE - MA2213 Lecture 11 PDE Topics ntroduction p...

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Unformatted text preview: MA2213 Lecture 11 PDE Topics ntroduction p. 451-452 oisson equation p. 453-466 Boundary conditions p. 453 Finite difference grid p. 454-456 MATLAB Program p. 456-458 Visualization of numerical results p. 459-466 ne-dimensional heat equation p. 466-481 Introduction Many phenomena in sciences and engineering epend on more than one variable. For example, n unknown function of a real-world problem sually depends on both time t and the location f the point (x,y,z).” p. 451 hysical laws, including the conservation of nergy, momentum and mass, the laws of lectricity and magnetism, thermodynamics, nd chemical kinetics, require that the partial erivatives of these functions satisfy certain partial differential) equations. Introduction ncreasingly, PDE’s are used to model biological nd social phenomena. The models include the law of supply and demand” in economics that etermines equilibrium prices of goods and ervices, the Black-Sholes equation for options rices in arbitrage-free financial markets, and aws that describe the evolution of population ensities that are used in epidemiology, ecology, nd population genetics. http://www.imbs.uci.edu/index.html Introduction xamples 2 2 2 2 2 ) , ( ), , ( f R y x y x y u x u ⊂ Ω ∈ = ∂ ∂ + ∂ ∂ Poisson equation ), , ( ), , ( f 2 2 > ∈ + ∂ ∂ = ∂ ∂ t L x t x x u a t u Heat equation ), , ( ), , ( f 2 2 2 2 > ∈ + ∂ ∂ = ∂ ∂ t L x t x x u a t u Wave equation Poisson Equation Boundary Conditions et be a planar domain, and denote its The boundary value problem 2 R ⊂ Ω oundary by . Ω ∂ Ω ∈ = ∂ ∂ + ∂ ∂ ) , ( ), , ( f 2 2 2 2 y x y x y u x u Ω ∂ ∈ = ) , ( ), , ( g y x y x u s called a Dirichlet problem because the value of...
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## This note was uploaded on 01/06/2012 for the course MA 2213 taught by Professor Michael during the Fall '07 term at National University of Singapore.

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L11_PDE - MA2213 Lecture 11 PDE Topics ntroduction p...

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