Is the following statement true or not? give a simple reason for your answer. (i) (1...

 

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Is the following statement true or not? give a simple reason for your answer. (i) (1 point) Any linear multistep method for the numerical solution of IVPS will have the error of the same order as the truncation error? (ii) (1 point) When a difference approximation is used to solve a BVP of linear 2nd-order ODEs, the consistency and stability of the method imply convergence. (iii) (1 point) The steepest descent method with a constant step size for the minimization problem can be seen as the forward Euler method for solving the associated gradient flow. (iv) (1 point) Explicit methods are always the top choices if one needs to solve a stiff ODE system. Is the following statement true or not? give a simple reason for your answer. (i) (1 point) Any linear multistep method for the numerical solution of IVPS will have the error of the same order as the truncation error? (ii) (1 point) When a difference approximation is used to solve a BVP of linear 2nd-order ODEs, the consistency and stability of the method imply convergence. (iii) (1 point) The steepest descent method with a constant step size for the minimization problem can be seen as the forward Euler method for solving the associated gradient flow. (iv) (1 point) Explicit methods are always the top choices if one needs to solve a stiff ODE system.