Course Information

Course Name	Turkish	Kısmi Türevli Diferansiyel Denklemlerin Sayısal Çözümleri
	English	PDE:Numerical Sol.
Course Code	MAT 488E	Credit	Lecture (hour/week)	Recitation (hour/week)	Laboratory (hour/week)
Semester	1	3	3	-	-
Course Language		English
Course Coordinator		Ersin Özuğurlu
Course Objectives		1. To introduce the basic concepts of the solutions of the partial differential equations, 2. To teach numerical methods to solve partial differential equations of various types.
Course Description		Initial and Boundary value problems; classification, well-posed problem. Finite difference method, discretization, Finite difference approximation to derivatives, The stability and convergence of finite difference method, convergence (Lax equivalent theorem), Fourier method and Matrix method for stability, Compatibility. Parabolic equations, an explicit finite difference approximation to one dimensional diffusion equation, Crank-Nicolson implicit method, Iterative point methods, Jacobi, Gauss-Seidel method. Hyperbolic equations; The quasilinear system, Method of characteristics, Explicit finite Difference method, MacCormics Method, Relaxation method, CFL condition, Lax-Wendroff method. Elliptic equations; Laplace equation, Error analysis by using the maximum principle, iterative methods, solutions of finite difference equations. Other methods; Finite volume method, finite element method, spectral method.
Course Outcomes		Students completing this course will be able to : İ. I.Classifies partial differential equations with respect to their certain properties, examines stability and convergence of the partial differential equations, İİ. By the use of the finite difference method, solves the partial differential equations of the parabolic type, İİİ. By the use of the finite difference method, solves the partial differential equations of the hyperbolic type, IV. By the use of the finite difference method, solves the partial differential equations of the elliptic type and learns the error analysis by using the maximum principle, V. V. By the use of other methods (finite volume method), solves the partial differential equations
Pre-requisite(s)		MAT331E Partial Differential equations
Required Facilities		.
Other		.
Textbook		K. W. Morton and D. F. Mayers, Numerical Solution of Partial Differential Equations, Cambridge University Press, New York, 1994.
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