Numerical Methods in Civil Engineering

This course attempts to give a broad background to numerical methods common to various branches of civil engineering. It starts with core concepts of error estimate and accuracy of numerical solutions. It then introduces the student to methods of solution of linear and nonlinear equations. Both direct and iterative solution methods are discussed. Next we introduce the numerical solution of partial differential equations, after a brief review of canonical partial differential equations and well known analytical techniques for their solution, stressing when and why numerical solutions are necessary. Finite difference operators are introduced and used to solve typical initial and boundary value problems. Following this we introduce the finite element method as a generic method for the numerical solution of partial differential equations. The concepts of weak form, finite element discretization, polynomial interpolation using Lagrange polynomials and numerical quadrature are introduced. Numerical integration in the time domain is discussed, emphasizing the key requirements of stability and accuracy of time integration algorithms. Finally we discuss integral equations and introduce numerical techniques for their solution. (from nptel.ac.in)