Question

Compute the coefficients in a multi-step method of the form xn+1 = xn + h[Afn +...

Compute the coefficients in a multi-step method of the form

xn+1 = xn + h[Afn + Bfn-2 + Cfn-4].

The formula should correctly integrate an equation x' = f(t, x) when the right hand side is of the form f(t, x) = a+b+ct2.

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Answer #1

Solution:-

Given that

The formula should correctly integrate an equation x' = f(t, x) when the right hand side is of the form f(t, x) = a+b+ct2.

Compute the coefficients in a multi-step method of the form

RHS

LHS

By comparing LHS and RHS

by solving these equations

we get

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