Synopsis :
This course discusses problem solving using numerical methods that involve non-linear equations, systems of linear equation, interpolation and curve fitting, numerical differentiation and numerical integration, eigenvalue problems, ordinary differential equations and partial differential equations.
Objectives:
On completing the course, students should be able to:
- Solve the nonlinear equations using bisection, simple iterative method and Newton method.
- Solve the linear system of equations using Gaussian elimination with/without pivoting, decomposition methods; Doolittle, Cholesky, Thomas, and Jacobi and Gauss-Seidel iterative methods.
- Solve the interpolation problem of given uniform data or non-uniform data using Lagrange interpolation polynomial, Newton’s divided difference Newton’s forward and least square curve fitting method including linearization technique.
- Estimate the range of eigenvalue using Gerschgorin circle theorem and find the eigenvalues and corresponding eigenvectors using power method and shifted power method.
- Produce the derivative of a function or table of function values up to fourth order using Taylor’s series and perform numerical integration of the function or table of function values using trapezoidal, Simpson’s 1/3 and Gaussian Quadrature (2 and 3 points).
- Solve the first order initial value problems using Euler, Taylor’s series (second and third order) and Runge-Kutta (RK2 and RK4) methods.
- Solve the boundary value problems (second and forth order) using finite difference methods with boundary condition with/without derivatives.
- Solve linear partial differential equations (first and second order) including elliptic, parabolic and hyperbolic using finite difference method.