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B.Tech. IT 3rd Sem Subject: Numerical Analysis & Computer Application
UNIT – 1 Approximations and Errors in Computation Errors and their analysis, Types of errors, General Error – formula, Errors in numerical computation. Curve fitting: Method of Least squares , fitting of a straight line, fitting of an exponential cures, polynomial fit : Non linear Regression ( second degree parabola ), Least Square Approximation, Method of moments.
UNIT – 2 Numerical Solution of Algebraic and Transcendental Equations Graphical method bisection Method, Secant Method, Regulfalsi Method, Newton Raphson Method, Iteration Method AITKEN’S Method Newton rate of convergence. Solution of a system of simultaneous linear algebraic Equations Direct method: Gauss elimination Method, Gauss Jordan method, triangularisation method crout’s method choleshy method, Ill conditioned system of equation and refinement of solution. Iterative methods: Jacobi Iterative Method, Gauss Seidel Iterative method, Successive over relaxation (SOR) method.
UNIT – 3 The Calculus of Finite Differences Finite differences, Difference formula, Operators and relation between operators. Differences of a polynomial factorial polynomial, Effect of an error on a difference table. Inverse Operator, Interpolation with equal intervals: Newton’s forward and backward interpolation formula. Central difference interpolation formula: gauss’s forward and backward interpolation formula, Sterling’s formula Bessel’s formula, Lap lace – Everett is formula, Choice of interpolation formula. Interpolation with Unequal intervals: Lagrange’s interpolation Newton’s difference formula, hermit’s interpolation, inverse interpolation,
UNIT – 4 Numerical Differentiation and Integration Numerical Differentiation Newton’s forward and Backward difference interpolation formula. Maximaand Minima of a Tabulated function, Numerical Integration: Newton cote’s quardrative formula Trapezoidol rule, Simpson is (1/3)rd and (3/8) th rule, Boole’s rule, weddle rule, Difference Equations: Definition, Order and degree of a diference equation, Linear difference equations, Difference equations reducible to Linear form. Simultaneous difference equations with constant coefficients Applications
UNIT – 5 Numerical solution of ordinary differential equation Taylor series method, Picard’s Method, Euler’s Method, Modified Euler method Runge’s method Runge Kutta method, Predict corrctor method, Milne’s method, Adam – Bashforth method. Numerical solution of partial differential Equations : Classification of P.D.E. of the second order Elliptic equations, Solution of Laplace equation, Solution of poisson’s Equation, Solution of elliptic equations by Relaxation method parabolicequations, Solution of one two dimensional heat equation, Hyperbolic Equations, Solution of wave equations.
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