Numerical Methods for Solving System of Hyperbolic Uncoupled Pdes
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Date
2019-07-02
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Addis Ababa University
Abstract
This thesis concentrates on numerical methods for solving hyperbolic un-
coupled PDEs systems with two independent variables (space and
time)and whose model problem is vt +Avx = 0 for which A is assumed to be a
diagonalized matrix;discusses the consistency,stability and convergence
based on the sup-norm, l2; x and discrete Fourier series methods on the
di erence equations; determine the stability and convergence region of the difference
equations so that the solution of the numerical di erence equation
is optimal.The given di erence equation is analysed on di erent time and space
schemes to nd the nature of the di erence equation and approximate solutions
with the given Initial Boundary Value Problem by taking sample schemes such
as FTFS, BTFS AND CTFS show that the schemes have similar precision and
accuracy in a stability region with the smallest grid size.
key words:-Numerical methods, Hyperbolic uncoupled PDEs, Model problem,
Diagonalized matrix, Consistency, Stability, Convergency, Sup-norm, `2; xNorm,
Discrete Fourier Transform,Di erence Equation, Di erence scheme, Initial Boundary
Value Problem(IBVP), precision and accuracy
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Keywords
Numerical Methods, Solving System, Hyperbolic, Uncoupled Pdes