An approximation method for the following ordinary differential equation: du -u(t); t e [1, ,4. dt...

 

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An approximation method for the following ordinary differential equation: du -âu(t); t e [1, ,4. dt with the initial condition u(0) = 4o leads to the following one-step formula: 24 - 6Ah 24 +18Ah+62 h² + 2'h' Show that the local error for the approximation obtained is 0(h) when comparing it with Taylor's series of e-Ah An approximation method for the following ordinary differential equation: du -âu(t); t e [1, ,4. dt with the initial condition u(0) = 4o leads to the following one-step formula: 24 - 6Ah 24 +18Ah+62 h² + 2'h' Show that the local error for the approximation obtained is 0(h) when comparing it with Taylor's series of e-Ah