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MAT 488E
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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
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Other
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Textbook
K. W. Morton and D. F. Mayers, Numerical Solution of Partial Differential Equations, Cambridge University Press, New York, 1994.
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