Solving a first order ODE using the Adomian Decomposition method

[chwala]

Homework Statement

how do we solve the ode $y'+y^2=-2, y(0)=0$ using adomian decomposition method?

Homework Equations

The Attempt at a Solution

$Ly = -2-y^2$
$y= 0 + L^{-1}[-2-y^2]$
$y_{0}= -2t$
$y_{1}= -L^{-1}[4t^2] = -4t^3/3$ are my steps correct so far in trying to get the Adomian Polynomials? am i following the correct steps?

 

[mjc123]

Oh, not a Pindaric ode then...

 

[fresh_42]

Homework Statement

how do we solve the ode $y'+y^2=-2, y(0)=0$ using adomian decomposition method?

Homework Equations

The Attempt at a Solution

$Ly = -2-y^2$
$y= 0 + L^-1[-2-y^2]$
$y[0]= -2t$
$y[1]= -L^-{1}[4t^2] = -4t^3/3$ are my steps correct so far in trying to get the Adomian Polynomials? am i following the correct steps?

I'm not used to this method, but your example is pretty close to the one on Wikipedia:
https://en.wikipedia.org/wiki/Adomian_decomposition_method

 

[Mark44]

I've never heard of the Adomian method, either, but I'm very familiar with using Laplace transforms and inverses to solve diff. equations.
Comments below.

The Attempt at a Solution

$Ly = -2-y^2$
$y= 0 + L^{-1}[-2-y^2]$
$y[0]= -2t$

The notation used in the wiki article whose link fresh_42 provided is $y_0$. Your notation confused me into thinking you meant y(0), which is given as 0.

$y[1]= -L^{-1}[4t^2] = -4t^3/3$ are my steps correct so far in trying to get the Adomian Polynomials? am i following the correct steps?

It looks good so far. How many terms in the polynomial do you need to get?

 

[chwala]

I've never heard of the Adomian method, either, but I'm very familiar with using Laplace transforms and inverses to solve diff. equations.
Comments below.
The notation used in the wiki article whose link fresh_42 provided is $y_0$. Your notation confused me into thinking you meant y(0), which is given as 0.
It looks good so far. How many terms in the polynomial do you need to get?

i want to try and get up to 5 terms of the polynomials and then probably compare with the analytical method/numerical methods...let me try and get the other polynomials then you can correct where necessary...

 

[chwala]

I've never heard of the Adomian method, either, but I'm very familiar with using Laplace transforms and inverses to solve diff. equations.
Comments below.
The notation used in the wiki article whose link fresh_42 provided is $y_0$. Your notation confused me into thinking you meant y(0), which is given as 0.
It looks good so far. How many terms in the polynomial do you need to get?

in life we are all learner's probably its good to admit that we may not know everything in math or rather i may know something which you do not know...now you know Adomian decomposition method has been used in solving first order and second order linear and non linear ode and pde. I am conversant with the laplace transforms...

 

[chwala]

i am getting
$y_{3}=-16t^5/15$
$y_{4}= -4t^7/5$
is this correct?

 

[chwala]

I've never heard of the Adomian method, either, but I'm very familiar with using Laplace transforms and inverses to solve diff. equations.
Comments below.
The notation used in the wiki article whose link fresh_42 provided is $y_0$. Your notation confused me into thinking you meant y(0), which is given as 0.
It looks good so far. How many terms in the polynomial do you need to get?

i just made some changes on the notation, sorry...