GATE Questions & Answers of Numerical Methods Electronics and Communication Engg

Consider the first order initial value problem 

y'=y+2x-x2,y0=1,0x<

with exact solution $ y\left(x\right)=x^2+e^x. $ For $ x=0.1, $ the percentage difference between the exact solution and the solution obtained using a single iteration of the second-order Runge-Kutta method with step-size $h = 0.1$ is __________

The Newton-Raphson method is used to solve the equation f(x) = x3 – 5x2 + 6x – 8 = 0. Taking the initial guess as x = 5, the solution obtained at the end of the first iteration is _____.

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

A polynomial f ( x ) = a 4 x 4 + a 3 x 3 + a 2 x 2 + a 1 x a 0 with all coefficients positive has

A numerical solution of the equation  fx=x+x-3=0 can be obtained using Newton- Raphson method. If the starting value is x = 2 for the iteration, the value of x that is to be used in the next step is

The recursion relation to solve x=e-x using Newton Raphson method is

For the function e-x, the linear approximation around x = 2 is:

The equation x3 - x2 + 4x - 4 = 0 is to be solved using the Newton-Raphson method. If x = 2 is taken as the initial approximation of the solution, then the next approximation using this method will be