UNIT I SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS
Solution of algebraic and transcendental equations
Fixed point iteration method
Newton Raphson method
Solution of linear system of equations
Gauss elimination method
Gauss Jordan method
Iterative methods of Gauss Jacobi and Gauss Seidel
Eigenvalues of a matrix by Power method and Jacobi’s method for symmetric matrices.
UNIT II INTERPOLATION AND APPROXIMATION
Interpolation with unequal intervals
Newton’s divided difference interpolation
Difference operators and relations
Interpolation with equal intervals
Newton’s forward and backward difference formulae.
UNIT III NUMERICAL DIFFERENTIATION AND INTEGRATION
Approximation of derivatives using interpolation polynomials
Numerical integration using Trapezoidal,
Simpson’s 1/3 rule
Two point and three point Gaussian quadrature formulae
Evaluation of double integrals by Trapezoidal and Simpson’s 1/3 rules.
UNIT IV INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS
Single step methods
Taylor’s series method
Modified Euler’s method
Fourth order Runge
Kutta method for solving first order equations
Multi step methods
Milne’s and Adams
Bash forth predictor corrector methods for solving first order equations.
UNIT V BOUNDARY VALUE PROBLEMS IN ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS
Finite difference methods for solving second order two
Point linear boundary value problems
Finite difference techniques for the solution of two dimensional Laplace’s and Poisson’s equations on rectangular domain
One dimensional heat flow equation by explicit and implicit (Crank Nicholson) methods
One dimensional wave equation by explicit method.
Upon successful completion of the course, students should be able to:
- Understand the basic concepts and techniques of solving algebraic and transcendental
- Appreciate the numerical techniques of interpolation and error approximations in various
intervals in real life situations.
- Apply the numerical techniques of differentiation and integration for engineering problems.
- Understand the knowledge of various techniques and methods for solving first and second order ordinary differential equations.
- Solve the partial and ordinary differential equations with initial and boundary conditions by using certain techniques with engineering applications.
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- Brian Bradie, “A Friendly Introduction to Numerical Analysis”, Pearson Education, Asia,
New Delhi, 2007.
- Gerald. C. F. and Wheatley. P. O., “Applied Numerical Analysis”, Pearson Education, Asia, 6th Edition, New Delhi, 2006.
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Edition, Prentice Hall, 1992.
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