This course provides an introduction to the numerical methods to solve various kinds of equations that students encounter in the field of engineering. The student will develop his/her own programs/subroutines for the numerical schemes taught in the course.
Numerical Methods in Linear Algebra:Direct and iterative solution techniques for simultaneous linear algebraic equations – Gauss elimination, Gauss-Jordon, LU Decomposition, QR Method, Jacobi and Gauss-Seidel MethodsEigenvalues and Eigenvectors – Power and inverse power method, householder transformation, physical interpretation of eigenvalues and eigenvectorsSolution of nonlinear algebraic equations: Bisection method, fixed-point iteration method, Newton-Raphson, Secant method, solution of system of nonlinear algebraic equationsInterpolation: Polynomial interpolation, Lagrange interpolating polynomial, Hermite interpolation, interpolation in 2 and 3 dimensionsNumerical Differentiation and IntegrationFinite difference formula using Taylor series, Differentiation of Lagrange polynomials, Simpson’s rule, Gauss-quadrature rule, Romberg method, multiple integralsNumerical solution of differential equationsOrdinary Differential Equations – Euler, Heun’s method and Stability criterion, second order and fourth order Runge-Kutta methods, Adams-Bashforth-Moulton method, system of ODEs and nonlinear ODEsPartial Differential Equations – Classification of PDEs, Elliptic equations, Parabolic equations (Transient diffusion equation), Hyperbolic equations (wave equation)
S. P. Venkateshan, Prasanna Swaminathan, Computational Methods in Engineering, Ane Books
Steven C. Chapra, Numerical Methods for Engineering, Mc-Graw Hill Education
Joe D Hoffman, Numerical Methods for Engineers and Scientists, Second Edition, Marcel Dekker (2001)
Gilbert Strang, Computational Science and Engineering, Wellesley-Cambridge Press