Abdi Tadesse (PhD)Kiyak Anteneh2019-11-152023-11-042019-11-152023-11-042019-07-02http://etd.aau.edu.et/handle/123456789/20131This 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 accuracyenNumerical MethodsSolving SystemHyperbolicUncoupledPdesThesis