Errors: Round-off error, Truncation error, Absolute error, Relative error, Percentage error; Ordinary Differential equations (ODE): Solutions of Initial Value Problems by Taylor Series, Euler, Improved Euler, Modified Euler, Runge-Kutta methods for First and second order differential equations, Multistep methods (Milne and Adams Bashforth). Consistency, stability and convergence aspects of the methods of IVP. Boundary Value Problems: Shooting and finite difference methods. Partial Differential Equations (PDE): Classification of PDEs, Finite difference approximations to partial derivatives, Numerical solutions of Elliptic, Parabolic and Hyperbolic partial differential equations. Solutions of Laplace equation by Leibmann’s iteration procedure, Poisson equation, Explicit, Crank-Nickolson, Du Fort Frankel methods for Parabolic PDE. Explicit formula for Hyperbolic PDE and Consistency, stability and convergence aspects of these methods. |