51. In numerical integration using Simpson's rule, the approximating function in interval is a
52. Using Simpson's 1/3 rule for numerical integration, the consecutive points are joined by a
53. The differential equation $$\frac{{{\text{dx}}}}{{{\text{dt}}}} = \frac{{4 - {\text{x}}}}{\tau },$$ with x(0) = 0 and the constant $$\tau $$ > 0, is to be numerically integrated using the forward Euler method with a constant integration time step T. The maximum value of T such that the numerical solution of x converges is
54. Match the following:
List-I
List-II
P. 2nd order differential equation
1. Runge-Kutta Method
Q. Non-linear algebraic equation
2. Newton-Raphson Method
R. Linear algebraic equation
3. Gauss Elimination
S. Numerical integration
4. Simpson's rule
List-I | List-II |
P. 2nd order differential equation | 1. Runge-Kutta Method |
Q. Non-linear algebraic equation | 2. Newton-Raphson Method |
R. Linear algebraic equation | 3. Gauss Elimination |
S. Numerical integration | 4. Simpson's rule |
55. Match the application to appropriate numerical method.
Application
Numerical Method
P1: Numerical integration
M1: Newton-Raphson Method
P2: Solution to a transcendental equation
M2: Runge-Kutta Method
P3: Solution to a system of linear equations
M3: Simpson's 1/3-rule
P4: Solution to a differential equation
M4: Gauss Elimination Method
Application | Numerical Method |
P1: Numerical integration | M1: Newton-Raphson Method |
P2: Solution to a transcendental equation | M2: Runge-Kutta Method |
P3: Solution to a system of linear equations | M3: Simpson's 1/3-rule |
P4: Solution to a differential equation | M4: Gauss Elimination Method |