Numerical Methods For Solving System Of Hyperbolic Uncoupled Pdes

This thesis concentrates on numerical methods for solving hyperbolic un-rncoupled PDEs systems with two independent variables (space andrntime)and whose model problem is vt +Avx = 0 for which A is assumed to be arndiagonalized matrix;discusses the consistency,stability and convergencernbased on the sup-norm, l2; x and discrete Fourier series methods on therndi erence equations; determine the stability and convergence region of the differencernequations so that the solution of the numerical di erence equationrnis optimal.The given di erence equation is analysed on di erent time and spacernschemes to nd the nature of the di erence equation and approximate solutionsrnwith the given Initial Boundary Value Problem by taking sample schemes suchrnas FTFS, BTFS AND CTFS show that the schemes have similar precision andrnaccuracy in a stability region with the smallest grid size.rnkey words:-Numerical methods, Hyperbolic uncoupled PDEs, Model problem,rnDiagonalized matrix, Consistency, Stability, Convergency, Sup-norm, `2; xNorm,rnDiscrete Fourier Transform,Di erence Equation, Di erence scheme, Initial BoundaryrnValue Problem(IBVP), precision and accuracy

Get Full Work

Report copyright infringement or plagiarism