National University of Sciences and Technology
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MTH-850 Advanced Numerical Analysis
Campus PNEC
Programs PG
Session Spring Semester 2017
Course Title Advanced Numerical Analysis
Course Code MTH-850
Credit Hours 3-0
Course Objectives Develop the understanding of advance methods in numerical analysis.
Detail Content Linear transformations on finite dimensional vector spaces. Invariant subspaces, rank, eigenvalues and eigenvectors. Canonical forms. Bilinear and multi linear forms. Matrices and linear algebra. General linear systems of equations, least squares minimization techniques, spectral decomposition. Interpolation theory and approximation of functions. Numerical solution of linear and nonlinear algebraic equations and eigenvalues problems. Curve fitting. Numerical integration, differentiation and solution of differential equations. Algorithms and computer programming. Cauchy – Kowalewski theorem. Characteristics, initial boundary value problems for parabolic and hyperbolic equations. Energy methods, boundary value problems for elliptic equations, potential theory. Green’s function, maximum principles, Schauder’s method. Linear multi-step methods and single step nonlinear methods for initial value problems. Consistency, stability and convergence. Finite difference, finite element, shooting method. Numerical methods for solving boundary and initial value problems for ordinary and partial differential equations. Specialized numerical methods for solution of Elliptic, Parabolic and Hyperbolic Partial Differential Equations. Applications of coordinate transformation in numerical solution of partial differential equation. Grid generation techniques.
Text/Ref Books
Time Schedule Spring Semester 2015
Faculty/Resource Person Dr S.K.N Zadi
Discipline: Mechanical Engineering
Specialization: Thermo-fluids