?′ (?) = −100?(?), ?(0) = y0 1) Find the condition for the step size dt...

?′ (?) = −100?(?), ?(0) = y₀

1) Find the condition for the step size dt such that the explicit Euler scheme converges to the exact solution to the given differential equation.

2) Find the condition for the step size dt such that the implicit Euler scheme converges to the exact solution to the given differential equation.

Expert Solution

Colby Messinger answered 2 years ago

Use a LaPlace transform to solve d^2x/dt^2+dx/dt+dy/dt=0 d^2y/dt^2+dy/dt-4dy/dt=0 x(0)=1,x'(0)=0 y(0)=-1,y'(0)=5

dy/dt +2y=t-1. ivp y0 =1 solve differntial equation

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