Consider the following method for integrating y' = f(t,y), y(to) = yo: h Yi+1 = Yi...

 

Transcribed Image Text:

Consider the following method for integrating y' = f(t,y), y(to) = yo: h Yi+1 = Yi + [f (ti, Yi) + f(ti+1, Yi+1]. (a) (1 point) Consider y'= -t sin(y). Write the above formula when applied to this ODE. (b) (2 points) To solve for yi+1 we need to apply Newton's method. Write this method for solving for yi+1. That is, write the function f and its derivative f' in f(xn) Xn+1 = Xn Consider the following method for integrating y' = f(t,y), y(to) = yo: h Yi+1 = Yi + [f (ti, Yi) + f(ti+1, Yi+1]. (a) (1 point) Consider y'= -t sin(y). Write the above formula when applied to this ODE. (b) (2 points) To solve for yi+1 we need to apply Newton's method. Write this method for solving for yi+1. That is, write the function f and its derivative f' in f(xn) Xn+1 = Xn

Answer rating: 100% (QA)

a For ytsiny well apply the given method yi1yih2ftiyifti1yi1 Substitute ft y with tsiny yi1yih2ti... View the full answer