Table 2 Numerical results of third order convergence test

\(S(t)\)

\(\xi_{1} = {{\left\| {s_{3} } \right\|} \mathord{\left/ {\vphantom {{\left\| {s_{3} } \right\|} {\left\| {s_{2} } \right\|}}} \right. \kern-0pt} {\left\| {s_{2} } \right\|}}\)

\({0}{\text{.7571642474}} < {1}\)

\(I(t)\)

\(\xi_{2} = {{\left\| {i_{3} } \right\|} \mathord{\left/ {\vphantom {{\left\| {i_{3} } \right\|} {\left\| {i_{2} } \right\|}}} \right. \kern-0pt} {\left\| {i_{2} } \right\|}}\)

\({0}{\text{.6704672834}} < {1}\)

\(V(t)\)

\(\xi_{3} = {{\left\| {v_{3} } \right\|} \mathord{\left/ {\vphantom {{\left\| {v_{3} } \right\|} {\left\| {v_{2} } \right\|}}} \right. \kern-0pt} {\left\| {v_{2} } \right\|}}\)

\({0}{\text{.3538198319}} < {1}\)

\(A(t)\)

\(\xi_{4} = {{\left\| {a_{3} } \right\|} \mathord{\left/ {\vphantom {{\left\| {a_{3} } \right\|} {\left\| {a_{2} } \right\|}}} \right. \kern-0pt} {\left\| {a_{2} } \right\|}}\)

\({0}{\text{.6417106679}} < {1}\)

\(Z(t)\)

\(\xi_{5} = {{\left\| {z_{3} } \right\|} \mathord{\left/ {\vphantom {{\left\| {z_{3} } \right\|} {\left\| {z_{2} } \right\|}}} \right. \kern-0pt} {\left\| {z_{2} } \right\|}}\)

\({0}{\text{.1324782061}} < {1}\)