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September 23, 2023


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Numerical Methods: Finite Difference Approach. Instructor: Dr. Ameeya Kumar Nayak, Department of Mathematics, IIT Roorkee.

This course is an advanced course offered to UG/PG student of Engineering/Science background. It contains solution methods for different class of partial differential equations. The convergence and stability analysis of the solution methods is also included. It plays an important role for solving various engineering and sciences problems. Therefore, it has tremendous applications in diverse fields in engineering sciences. (from nptel.ac.in)

Course Curriculum

  • Lecture 01 – Introduction to Numerical Solutions Unlimited
  • Lecture 02 – Numerical Solution of Ordinary Differential Equations Unlimited
  • Lecture 03 – Numerical Solution of Partial Differential Equations Unlimited
  • Lecture 04 – Finite Differences using Taylor Series Expansion Unlimited
  • Lecture 05 – Polynomial Fitting and One-sided Approximation Unlimited
  • Lecture 06 – Solution of Parabolic Equations Unlimited
  • Lecture 07 – Implicit and Crank-Nicolson Method for Solving 1D Parabolic Equations Unlimited
  • Lecture 08 – Compatibility, Stability and Convergence of Numerical Methods Unlimited
  • Lecture 09 – Stability Analysis of Crank-Nicolson Method Unlimited
  • Lecture 10 – Approximation of Derivative Boundary Conditions Unlimited
  • Lecture 11 – Solution of Two Dimensional Parabolic Equations Unlimited
  • Lecture 12 – Solution of 2D Parabolic Equations using ADI Method Unlimited
  • Lecture 13 – Elliptic Equations: Solution of Poisson Equation Unlimited
  • Lecture 14 – Solution of Poisson Equation using Successive over Relaxation (SOR) Method Unlimited
  • Lecture 15 – Solution of Poisson Equation using ADI Method Unlimited
  • Lecture 16 – Solution of Hyperbolic Equations Unlimited
  • Lecture 17 – Stability Analysis of Hyperbolic Equations Unlimited
  • Lecture 18 – Characteristics of PDEs and Solution of Hyperbolic Equations Unlimited
  • Lecture 19 – Lax-Wendroff Method Unlimited
  • Lecture 20 – Lax-Wendroff Method (cont.) Unlimited

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