SSCE2393 Numerical Methods (SPACE MIRI)

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:

  1. Solve the nonlinear equations using bisection, simple iterative method and Newton method.
  2. Solve the linear system of equations using Gaussian elimination with/without pivoting, decomposition methods; Doolittle, Cholesky, Thomas, and Jacobi and Gauss-Seidel iterative methods.
  3. 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.
  4. Estimate the range of eigenvalue using Gerschgorin circle theorem and find the eigenvalues and corresponding eigenvectors using power method and shifted power method.
  5. 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).
  6. Solve the first order initial value problems using Euler, Taylor’s series (second and third order) and Runge-Kutta (RK2 and RK4) methods.
  7. Solve the boundary value problems (second and forth order) using finite difference methods with boundary condition with/without derivatives.
  8. Solve linear partial differential equations (first and second order) including elliptic, parabolic and hyperbolic using finite difference method.
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