Dr. Hanif Durad 2
Lecture Outline
๎Partial Differential Equations
๎Numerical Methods for PDEs
๎Sparse Linear Systems
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Partial Differential Equations part 1-Computational Physics-Lecture Slides, Slides of Computational Physics
This lecture is for Computational Physics course. It was delivered by Dr. Hanif Durad at Pakistan Institute of Engineering and Applied Sciences, Islamabad (PIEAS). It includes: Partial, Differential, Advection, Equation, Numerical, Methods, Sparse, Linear, Systems, Characteristics
Typology: Slides
2011/2012
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Dr. Hanif Durad
Lecture Outline
Partial Differential Equations
Numerical Methods for PDEs
Sparse Linear Systems
(1/2)Partial Differential Equations
Dr. Hanif Durad
(1/2)Example: Advection Equation
Dr. Hanif Durad
(1/2)Example: Advection Equation
Dr. Hanif Durad
Classification of PDEs (1/3)
Dr. Hanif Durad
Classification of PDEs (2/3)
Dr. Hanif Durad
Assignment-
Find analytical solution of heat equation
Dr. Hanif Durad
t
xx
u Cu
u t u x t
x
u x
x
x
Using C=
Semidiscrete MethodsTime-Dependent Problems
Semidiscrete Methods
Dr. Hanif Durad
MethodSemidiscrete Finite Difference
Dr. Hanif Durad
Stiffnes (MOL)
Dr. Hanif Durad
Assignment-
equationUse method of line to solve the heat
Dr. Hanif Durad
t
xx
u Cu
u t u x t
x
u x
x
x
Using x=0.2 and n=
(2/4)Semidiscrete Collocation Method
Dr. Hanif Durad
(3/4)Semidiscrete Collocation Method
Dr. Hanif Durad