We first consider the following single degree of freedom (SDOF) problem: i + Au= 10 cos(t/10)...

   

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We first consider the following single degree of freedom (SDOF) problem: i + Au= 10 cos(t/10) 20= 100 where the exact solution is given by: 1000X - (10- 1+100X² and the numerical error is defined as: u(t) = Error = -At exp + 100[10X cos(t/10) + sin(t/10)] 1 + 100X² Numerical Exact Exact (1) (2) (3) Define the time step length: h= 0.01, and 1. Use Explicit Euler Forward scheme to get u at t₁, t2 and t3 and the associated errors (20 points) 2. Use RK 4 to solve this problem to get u at t₁, t2 and t3 and the associated errors (20 points) 3. Use Implicit Euler Backward to to get u at t₁, t2 and t3 and the associated errors (20 points) We first consider the following single degree of freedom (SDOF) problem: i + Au= 10 cos(t/10) 20= 100 where the exact solution is given by: 1000X - (10- 1+100X² and the numerical error is defined as: u(t) = Error = -At exp + 100[10X cos(t/10) + sin(t/10)] 1 + 100X² Numerical Exact Exact (1) (2) (3) Define the time step length: h= 0.01, and 1. Use Explicit Euler Forward scheme to get u at t₁, t2 and t3 and the associated errors (20 points) 2. Use RK 4 to solve this problem to get u at t₁, t2 and t3 and the associated errors (20 points) 3. Use Implicit Euler Backward to to get u at t₁, t2 and t3 and the associated errors (20 points)