how to use Choleski method MATLAB, solve the following linear equations
Using Choleski method MATLAB, solve the following linear equations Solution : >> A=[2 -1 0;-1 2 -1;0 -1 1] A = 2 -1 0 -1 2 -1 0 -1 1…
How do you find singular value decomposition of a complex matrix?
Question : How do you find singular value decomposition of a complex matrix? Solution: Singular value decomposition: Let \[A\in M_{m\times n}\left(C\right)\] be any complex matrix. Then we define singular value…
Solved find the sum of the series (1/n+1/(n+1)+1/(n+2)+…..+1/4n as limit n approaches infinity
Question : Find the sum of the series 1/(n+1)+1/(n+2)+…..+1/4n as limit n approaches infinity Solution : Let the sum of the series as \[L=\lim_{n\rightarrow\infty}{\left[\frac{1}{n}+\frac{1}{n+1}+\frac{1}{n+2}+\ldots..+\frac{1}{4n}\right]\ }\] \[L=\lim_{n\rightarrow\infty}{\left[\frac{1}{n}+\frac{1}{n+1}+\frac{1}{n+2}+\ldots..+\frac{1}{n+3n}\right]\ }\] \[=\lim_{n\rightarrow\infty}{\frac{1}{n}\left[\frac{n}{n}+\frac{n}{n+1}+\frac{n}{n+2}+\ldots..+\frac{n}{n+3n}\right]\ }\] \[=\lim_{n\rightarrow\infty}{\frac{1}{n}\left[\frac{1}{1+\frac{0}{n}}+\frac{1}{1+\frac{1}{n}}+\frac{1}{1+\frac{2}{n}}+\ldots..+\frac{1}{1+\frac{3n}{n}}\right]\…
solve following second order ode numerically matlab
Question : Solve following second order ode numerically matlab \[\frac{d^2y}{dt^2}+\frac{dy}{dt}+y=2t+3\sin{\left(t\right)} , y\left(0\right)=2,\ y^\prime\left(0\right)=3 \] in the interval [0, 10] and plot the solution. Solution : To Solve given second order…
how to convert following second order ode into a system of first order ODEs
Question ; Convert following second order ode into a system of first order ODEs \[\frac{d^2y}{dt^2}+\frac{dy}{dt}+y=2t+3\sin{\left(t\right)} , y\left(0\right)=2,\ y^\prime\left(0\right)=3 \] Solution : Given second order ODE \[\frac{d^2y}{dt^2}+\frac{dy}{dt}+y=2t+3\sin{\left(t\right)} \] (1) Subject to…
solved find first five steps of Newtons method to solve x^3+e^x-2=0 with initial guess x0=0
Introduction : Here we shall apply Newtons method to solve x^3+e^x-2=0 with initial guess x0=0. Newton method is an numerically approximation to the solution of an equation provided an initial…
Solved Convert Van Der Pol Oscillator into system of first order ODEs
Introduction : Van Der Pol Oscillator is a second order ODE. This equation is converted into a system of first order ODEs. Question : Convert Van Der Pol Oscillator \[\frac{d^2x}{dt^2}-3\left(1-x^2\right)\frac{dx}{dt}+x=0…
prove that error between approximating function and first three terms of power series expansion is less than 1/1500
Introduction: In this solution, we prove that error between approximating function and first three terms of power series expansion is less than 1/1500. Question: Power series expansion of a function…
How to solve x^2-3=0 by secant method MATLAB
Introduction: In this solution we will solve x^2-3=0 by secant method MATLAB program We will also determine the error at each iteration and estimate the root of the equation. Question:…
how to find rate of convergence of newton’s method for solving of f(x)=x^4 with x0=1
Introduction : This is the step by step solution to the question how to find rate of convergence of newton's method for solving of f(x)=x^4 with x0=1 Question : find…