Finite difference schemes for partial differential equations - explicit and implicit schemes Consistency, stability and convergence - stability analysis by matrix method and von Neumann method, Lax's equivalence theorem Finite difference schemes for initial and boundary value problems - FTCS, backward Euler and Crank-Nicolson schemes, ADI methods, Lax Wendroff method, upwind scheme CFL conditions Finite element method for ordinary differential equations - variational methods, method of weighted residuals, finite element analysis of one-dimensional problems.

Numerical techniques for solving differential equations by approximating derivatives with finite differences.

Finite difference methods convert ordinary differential equations (ODE) or partial differential equations (PDE), which may be nonlinear, into a system of linear equations that can be solved by matrix algebra techniques. Today, FDM are one of the most common approaches to the numerical solution of PDE, along with finite element methods.

G. D. Smith, Numerical Solutions to Partial Differential Equations, Oxford University Press, 3rd Edn

J. C. Strikwerda, Finite Difference Schemes and Partial Differential Equations, SIAM, 2004

K. W. Morton and D. F. Mayers, Numerical Solution of Partial Differential Equations, Cambridge University Press, 2nd Edn., 2005

C. Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method, Dover Publications, 2009