Recent activity in Numerical Methods

Consider the equation $\dfrac{d y}{d x}=\dfrac{1}{x}$The value of the integral $\int_{1}^{2} d y$ using trapezoidal method and interval $h=0.25$ is $\_\_\_\_$. (rounded o...

Consider a nonlinear algebraic equation, $e^{x}-2=0$. Using the Newton-Raphson method, with the initial guess of $x_{0}=1$, the approximated value of the root of the equa...

The absolute relative error in evaluating the integral $\int_0^1 x^2 d x$ by the trapezoidal rule with the step size $0.25$ is $\%$ $\_\_\_\_\_\_\_\_$ (rounded off to $2$...

Consider a nonlinear algebraic equation, $x\ln x + x – 1 = 0.$ Using the Newton-Raphson method, with the initial guess of $x_{0} = 3,$ the value of $x$ after one iteratio...

Consider the ordinary differential equation $\dfrac{dy}{dx} = f(x,y) = 2x^{2} – y^{2}.$ If $y(1)=1,$ the value(s) of $y(1.5),$ using the Euler’s implicit method $\left[y_...

$\int _{-1}^{1}\:f\left ( x \right )dx$ calculated using trapezoidal rule for the values given in the table is ______ (rounded off to $2$ decimal places).$$\begin{array}{...