GATE ECE
Engineering Mathematics
Numerical Methods
Previous Years Questions

## Marks 1

The Newton-Raphson method is used to solve the equation $$f\left( x \right) = {x^3} - 5{x^2} + 6x - 8 = 0.$$ Taking the initial guess as $$x=5$$, the ...
A numerical solution of the equation $$f\left( x \right) = x + \sqrt x - 3 = 0$$ can be obtained using Newton $$-$$ Raphson method. If the starting v...
Consider a differential equation $${{dy\left( x \right)} \over {dx}} - y\left( x \right) = x\,\,$$ with initial condition $$y(0)=0.$$ Using Euler's fi...
The recursion relation to solve $$x = {e^{ - x}}$$ using Newton $$-$$ Raphson method is
The equation $${x^3} - {x^2} + 4x - 4 = 0\,\,$$ is to be solved using the Newton - Raphson method. If $$x=2$$ taken as the initial approximation of th...
Given the differential equation $${y^1} = x - y$$ with initial condition $$y(0)=0.$$ The value of $$y(0.1)$$ calculated numerically upto the third pla...

## Marks 2

Starting with $$x=1,$$ the solution of the equation $$\,{x^3} + x = 1,\,\,$$ after two iterations of Newton-Raphson's method (up to two decimal places...
Consider the first order initial value problem $$\,y' = y + 2x - {x^2},\,\,y\left( 0 \right) = 1,\,\left( {0 \le x < \infty } \right)$$ With exact ...
The ordinary differential equation $$\,\,{{dx} \over {dt}} = - 3x + 2,\,\,$$ with $$x(0)=1$$ is to be solved using the forward Euler method. The larg...
Match the application to appropriate numerical method Applications $$P1:$$ Numerical integration $$P2:$$ Solution to a transcendental equation $$P3:... Match the following and choose the correct combination Group$$-{\rm I}E.$$Newton$$-$$Raphson method$$F.$$Runge-Kutta method$$G. Sim...
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