MA8491 NUMERICAL METHODS (NM)
Prepared by
S.Santhosh (Admin)
Important questions
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UNIT -1
1.Gauss elimination method , Pivoting ,
Gauss Jordan method
2.Iterative methods of Gauss Jacobi and Gauss Seidel
UNIT-2
1. Newton’s forward and backward difference
2.Lagrange's interpolation,Newton’s divided difference
interpolation
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UNIT-3
1.Numerical integration using
Trapezoidal, Simpson’s 1/3 rule **
2. Rombergs method **
UNIT-4
1.Fourth order Runge **
2. Kutta method for solving first order equations
3. Taylors method
UNIT-5
1.Two dimensional Laplace’s and Poisson’s equations **
on rectangular domain
2.One dimensional heat flow equation by explicit and implicit
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*These questions are expected for the exams This may or may not be asked for exams All the best.... from admin Santhosh
Thanks for your love and support guys keep supporting and share let the Engineers know about Us and leave a comment below for better improvements If there is any doubt feel free to ask me I will clear if I can or-else I will say some solutions ..get me through WhatsApp for instant updates ~$tuff$£ctorSYllabuSUNIT 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 – Pivoting - 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 - Lagrange's interpolation – Newton’s divided difference interpolation – Cubic Splines - 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 – Romberg’s Method - 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 - Euler’s 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.
Contact uS
*These questions are expected for the exams This may or may not be asked for exams
All the best.... from admin Santhosh
Thanks for your love and support guys keep supporting and share let the Engineers know about Us and leave a comment below for better improvements
If there is any doubt feel free to ask me I will clear if I can or-else I will say some solutions ..get me through WhatsApp for instant updates ~$tuff$£ctorUNIT 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 – Pivoting - 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 - Lagrange's interpolation – Newton’s divided difference interpolation – Cubic Splines - 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 – Romberg’s Method - 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 - Euler’s 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.