Solution of Non-Linear Equations:
Numerical methods for solution of nonlinear equations. Regula-falsi method, Newton’s Method. Rate and Conditions of Convergence for iterative and Newton’s method.
System of Linear Equation:
Gaussian elimination method. Triangular decomposition method and its various forms. Iterative methods (Jacobi, Gauss- Seidel) for solving system of linear equations.
Finite and divided differences. Newton’s formula for interpolation. Inverse interpolation.
Interpolation with unequal intervals, Cecteral difference interpolation formulas (Gauss & Strrilling).
Various method including Aitkins and Lagrange interpolation, error estimates formulae for interpolation and its applications.
Trapezoidal, Simpson and quadratic formula for evaluating integrals with error estimates. Difference and Numerical solution of Differential Equations:
Formulation of difference equations, solution of linear (homogeneous and non- homogeneous) difference equations with constant coefficients, Euler and the modified Euler method.
To familiarize students with different numerical methods techniques used to find solution of different types of problems.
Course Learning Outcomes
Students will get familiar to different numerical methods techniques for different types of numerical problems. This will enhance their ability to find solution of different mathematical problems.
Introduction to Differential Equations by mathematics foundation 1
Classification of Differential Equations by mathematics foundation 2
Euler’s Method by Ally Learn
Modified Euler’s Method by Ally Learn
Midpoint Method by Ally Learn
Difference Equations Introduction and Solution of Homogeneous Difference Equation
Solution of Non Homogeneous Difference Equations Part 01
Solution of Non Homogeneous Difference Equations Part 02
Book Title : Applied Numerical Analysis
Author : C. Gerald, & O.H. Patrick
Edition : 7th
Publisher : Addison- Wesley publication Company
Book Title : Numerical Mathematical Analysis
Author : James B. Scarborough
Publisher : John Hopkins press