\contentsline {section}{\numberline {1}Euler's method and beyond}{2}{section.1}%
\contentsline {subsection}{\cref {setting1}}{2}{section*.2}%
\contentsline {subsection}{\cref {prob1}}{2}{section*.3}%
\contentsline {subsection}{\cref {def:converge}}{3}{section*.4}%
\contentsline {subsection}{\cref {prob2}}{3}{section*.5}%
\contentsline {subsection}{\cref {lem:gronwall}}{3}{section*.6}%
\contentsline {subsection}{\cref {prob3}}{4}{section*.7}%
\contentsline {subsection}{\cref {prob4}}{5}{section*.8}%
\contentsline {subsection}{\cref {setting2}}{5}{section*.9}%
\contentsline {subsection}{\cref {prob5}}{6}{section*.10}%
\contentsline {subsection}{\numberline {1.1}An exploration of the linear case}{7}{subsection.1.1}%
\contentsline {subsection}{\cref {def:mat_exp}}{7}{section*.11}%
\contentsline {subsection}{\cref {def:mat_det}}{7}{section*.12}%
\contentsline {subsection}{\cref {def:mat_trace}}{7}{section*.13}%
\contentsline {subsection}{\cref {lem:mat_exp1}}{7}{section*.14}%
\contentsline {subsection}{\cref {prob:mat_exp1}}{8}{section*.15}%
\contentsline {subsection}{\cref {prob:mat_exp2}}{9}{section*.16}%
\contentsline {section}{\numberline {2}Multistep methods}{10}{section.2}%
\contentsline {subsection}{\cref {setting_2_1}}{10}{section*.17}%
\contentsline {subsection}{\cref {def:order}}{11}{section*.18}%
\contentsline {subsection}{\cref {lemma:multi}}{11}{section*.19}%
\contentsline {section}{\numberline {3}Runge-Kutta methods}{13}{section.3}%
\contentsline {section}{\numberline {4}Stiff equations}{13}{section.4}%
\contentsline {subsection}{\cref {def:stable}}{13}{section*.20}%
\contentsline {subsection}{\cref {problem_stiff}}{13}{section*.21}%
\contentsline {section}{\numberline {5}Geometric numerical integration}{14}{section.5}%
\contentsline {section}{\numberline {6}Error control}{14}{section.6}%
\contentsline {section}{\numberline {7}Nonlinear algebraic systems}{14}{section.7}%
\contentsline {section}{\numberline {8}Finite difference schemes}{14}{section.8}%
\contentsline {subsection}{\cref {prob:finite_difference}}{14}{section*.22}%