numerical-methods

In the following differential equation, the numerically obtained value of y(t), at t =1, is ________ (Round off to 2 decimal places). $\frac{dy}{dt} = \frac{e^{-at}}{2 + at}$, α =...

Only one of the real roots of f(x) = x^6 - x - 1 lies in the interval 1 ≤ x ≤ 2 and bisection method is used to find its value. For achieving an accuracy of 0.001, the required min...

The per-unit power output of a salient-pole generator which is connected to an infinite bus, is given by the expression, P = 1.4 sin $$\delta $$ + 0.15 sin 2$$\delta $$, where $$\d...

The function $$f\left( x \right) = {e^x} - 1\,\,$$ is to be solved using Newton $$-$$ Raphson method. If the initial value of $${x_0}$$ is taken $$1.0,$$ then the absolute error ob...

When the Newton-Raphson method is applied to solve the equation $$\,\,f\left( x \right) = {x^3} + 2x - 1 = 0,\,\,$$ the solution at the end of the first iteration with the initial...

Solution, the variable $${x_1}$$ and $${x_2}$$ for the following equations is to be obtained by employing the Newton $$-$$ Raphson iteration method equation (i) $$10\,{x_2}\,\sin \...

Let $$\,{x^2} - 117 = 0.\,\,$$ The iterative steps for the solution using Newton -Raphson's method is given by

Equation $${e^x} - 1 = 0\,\,$$ is required to be solved using Newton's method with an initial guess $$\,\,{x_0} = - 1.\,\,$$ Then after one step of Newton's method estimate $${x_1}...

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 place of decimal by the $${2^{nd}...