Shooting method for non-linear equation

In summary, the shooting method can be used to solve non-linear equations by finding the value of t at each iteration using the given formula. To find y(b,t), the Euler method can be used, as demonstrated in the example question. If the values for y(b,t0) and y(b,t1) are not given, they can be found by using the given values for t0 and t1.
  • #1
sigh1342
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shooting method for non-linear equation(urgent)

Homework Statement


for shooting method , in non-linear equation, we're find
$$t_{k}=t_{k-1}-\frac{[y(b,t_{k-1})-β](t_{k-1}-t_{k-2})}{y(b,t_{k-1})-y(b,t_{k-2})}$$
but how can we find the $$y(b,t_{k})$$ ?
I am suppose to use Euler method for it , but I'm confused,
for example , the question is $$y''=-(y')^2-y+lnx , 1≤x≤2 , y(1)=0, y(2)=ln2$$
suppose $$t_{0}=3, y(2,t_{0})=2.775, t_{1}=0.7, y(2,t_{1})=0.5775 $$we can find $$t_{2}=0.72105$$ then how can we find $$y(2,t_{2})$$ ?with Euler method , with h=0.5,
and I also want to know if the question didn't give what the $$y(b,t_{0})$$ , and $$y(b,t_{1})$$ is , how can I find them in the case , I know what $$t_{0} $$ and $$t_{1}$$ is , sorry for the poor
English but the way.

Homework Equations





The Attempt at a Solution

 
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  • #2
it's ok now , I got it , no need to answer this post , thank you lol
 

FAQ: Shooting method for non-linear equation

What is the shooting method for non-linear equations?

The shooting method is a numerical technique used to solve non-linear equations. It involves converting the differential equation into a system of first-order equations, and then solving the system using an initial value solver.

How does the shooting method work?

The shooting method works by guessing an initial condition for the unknown variable in the non-linear equation, and then solving the resulting system of first-order equations using an initial value solver. If the resulting solution does not satisfy the original non-linear equation, the initial guess is adjusted and the process is repeated until a satisfactory solution is obtained.

What are the advantages of using the shooting method?

One advantage of using the shooting method is that it can be applied to a wide range of non-linear equations, including those that cannot be solved analytically. It is also relatively easy to implement and does not require complex mathematical techniques.

What are the limitations of the shooting method?

The shooting method may not always converge to a solution, especially if the initial guess is far from the actual solution. In addition, for some non-linear equations, the shooting method may require a large number of iterations to obtain a satisfactory solution.

How is the shooting method different from other numerical methods?

Unlike other numerical methods, such as the finite difference or finite element methods, the shooting method does not require the equation to be discretized. It also does not require the calculation of derivatives, which can be computationally expensive. However, it may not be as accurate as these other methods.

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