A Note on Some Numerical Approaches to Solve a Neuron Networks Model

Table 1

Order	Formula	Local truncation error
1	𝜃^𝑖+1=𝜃^𝑖+Δ𝑡𝐵^−1𝑓𝜃^𝑖	Δ𝑡^22𝜃^′′(𝜉)
2	𝜃^𝑖+2=𝜃^𝑖+1+Δ𝑡2𝐵^−13𝑓𝜃^𝑖+1−𝑓𝜃^𝑖	5Δ𝑡^3𝜃12^′′′(𝜉)
3	𝜃^𝑖+3=𝜃^𝑖+2+Δ𝑡𝐵12^−123𝑓𝜃^𝑖+2−16𝑓𝜃^𝑖+1+5𝑓𝜃^𝑖	3Δ𝑡^48𝜃^(4)(𝜉)
4	𝜃^𝑖+4=𝜃^𝑖+3+Δ𝑡𝐵24^−155𝑓𝜃^𝑖+3−59𝑓𝜃^𝑖+2+37𝑓𝜃^𝑖+1−9𝑓𝜃^𝑖	251Δ𝑡^5𝜃720^(5)(𝜉)
5	𝜃^𝑖+5=𝜃^𝑖+4+Δ𝑡𝐵720^−11901𝑓𝜃^𝑖+4−2774𝑓𝜃^𝑖+3+2616𝑓𝜃^𝑖+2−1274𝑓𝜃^𝑖+1+251𝑓𝜃^𝑖	95Δ𝑡^6𝜃2888^(6)(𝜉)