i) The most general \(\displaystyle k\)-step Linear Multistep Method has the form
\(\displaystyle \alpha_k\ y_{n+k}\ +\ ...\ +\ \alpha_0y_n\ =\ h[\beta_kf_n+k\ +\ ...\ +\ \beta_0\f_n]\).
Define the order of accuracy in terms of the linear difference operator
\(\displaystyle \L[y(x);h]\) and give the forms of the coefficients \(\displaystyle c_q\) of \(\displaystyle h^qy^{(q)}(x)\) in \(\displaystyle \L[y(x);h]\)
ii) Calculate the order of accuracy for the explicit Linear Multistep Method
\(\displaystyle y_{n+4}\ -\ y_{n+3}\ =\ \frac{h}{24}(55f_{n+3}\ -\ 59f_{n+2}\ +\ 37f_{n+1}\ -\ 9f_n)\)
The notes for this section are particularly confusing - in dire need of an answer.
\(\displaystyle \alpha_k\ y_{n+k}\ +\ ...\ +\ \alpha_0y_n\ =\ h[\beta_kf_n+k\ +\ ...\ +\ \beta_0\f_n]\).
Define the order of accuracy in terms of the linear difference operator
\(\displaystyle \L[y(x);h]\) and give the forms of the coefficients \(\displaystyle c_q\) of \(\displaystyle h^qy^{(q)}(x)\) in \(\displaystyle \L[y(x);h]\)
ii) Calculate the order of accuracy for the explicit Linear Multistep Method
\(\displaystyle y_{n+4}\ -\ y_{n+3}\ =\ \frac{h}{24}(55f_{n+3}\ -\ 59f_{n+2}\ +\ 37f_{n+1}\ -\ 9f_n)\)
The notes for this section are particularly confusing - in dire need of an answer.
