Show that the solution of this differential equation is the logistic function

SKU: assim1 Category:

Test your algorithm on a variety of nonlinear functions.How does it compare to other algorithms?


Order Now

A modification to the regula falsi method uses two starting estimates that must bracket the root. The algorithm is as follows:

1.a.Given two starting estimates, x1 and x2 that bracket the root, compute the mid point, xm = (x1 + x2)/2.

b.Compute the corresponding function evaluations for these three points: y1 = f(x1), y2 = f(x2) and ym = f(xm).


c. Compute s = rot If s = 0, then set x = xm and stop. Otherwise continue.


d. Update the estimate



e. Tighten the bracket by keeping xn and one of x1, x2 or xm with:

If xm and xn bracket the root, set x1 = xm and x2 = xn

Else, if x1 and xn bracket the root, set x2 = xn

Else, it must be the case that xn and x2 bracket the root, so set x1 = xn.


f. Continue by returning to step 1.

Write a Matlab root finding routine using the following algorithm. Test your algorithm on a variety of nonlinear functions. How does it compare to other algorithms?



2. A simple model of the spread of disease gives


where P(t) represents the number of individuals in the population who are infected, and C is the constant size of the total population.


(a) Show that the solution of this differential equation is the logistic function.

(b) Suppose that the parameter k fluctuates (perhaps because the population is more susceptible during certain seasons). Solve the modified problem


with P(0) = 10, k = 2, C = 200.



3. Solve the Bessel equation of order one,


starting with y(1) = 1 and y 0 (1) = 0 on 1 ≤ x ≤ 4



4. The motion of one body around another, such as a comet orbiting around the sun, can be described by the system

where the distance r =r1


With distance in AU (1 AU = 1.496 × 1011 m) and time in years, we have K ≈ 40 for an object rotating around the sun.

Take as initial conditions x(0) = 1, x0 (0) = 0 and y(0) = 0, y0 (0) = 2, and solve for 0 ≤ t ≤ 4.


Investigate the effects of different values of y 0 (0).



5. The equations for the deflection y and rotation z or a simply supported beam with a uniformly distributed load of intensity 9 · 103 N/ft and bending moment M(x) = 10x−x² can be expressed as


where E is the modulus of elasticity, and I is the moment of inertia of the cross section of the beam.

Taking EI = 1.6 · 107 N and y(0) = 0 and z(0) = −0.02, find y and z for 0 < x < 10.



6. Numerically compare the following 4th order Runga-Kutta-Gill method with the classical Runge-Kutta method.



Writing your homework and assignments all on your own is a difficult task. So, Assignments4u has made it easy for students by helping them in writing their assignments. Assignments4u will assist you in completing your tasks, and you can approach us with all your assignment, homework, and essay writing requirements.

We have over 4350+ experienced writers working as experts in different streams of study. Get all your academic doubts clarified and take pride in learning subjects like history, math’s or law. Our assignment help and essay help is available in countries like USA, Australia, New Zealand, Singapore and many more. Get accounting assignment help, corporate nursing assignment help, marketing assignment help or else statistics assignment help in exchange for a nominal price.


There are no reviews yet.

Be the first to review “Show that the solution of this differential equation is the logistic function”

Your email address will not be published. Required fields are marked *

Sorry no more offers available

When assignments gets tough, get tougher

Want a fresh solution like this one? 
We are available 24/7
Get CallBack