Collocation Method via Jacobi Polynomials for Solving Nonlinear Ordinary Differential Equations

Table 2

The solution of our example for different values of 𝛼 and 𝛽.

𝛼=0,; 𝛽=0	𝑦=−0.00000000000000001119663700028745952445299264438𝑃0^(0,0)(𝑥)+0.91522505937265707954150015923236𝑃1^(0,0)(𝑥)−0.000000000000000022393274000574919048905985288767𝑃2^(0,0)(𝑥)−0.059677652961529090927417051547721𝑃3^(0,0)(𝑥).
𝛼=−0.4,; 𝛽=−0.4	𝑦=−0.000000000000000009996746174510901192865699495𝑃0^(−0.4,−0.4)(𝑥)+0.89426538703542076709570198303656𝑃1^(−0.4,−0.4)(𝑥)−0.000000000000000011996095223297443607007612548232𝑃2^(−0.4,−0.4)(𝑥)−0.04198983897503790669842860235471𝑃3^(−0.4,−0.4)(𝑥).
𝛼=−0.5,; 𝛽=−0.5	𝑦=+0.0000000000000000311183604968765645740547197244𝑃0^(−0.5,−0.5)(𝑥)+0.88795403952304732584548430952028𝑃1^(−0.5,−0.5)(𝑥)+0.000000000000000031118360496876564574054719724411𝑃2^(−0.5,−0.5)(𝑥)−0.036586425139067737724980961913629𝑃3^(−0.5,−0.5)(𝑥).
𝛼=−0.4,; 𝛽=0.6	𝑦=+0.40613910584685335757685249174382𝑃0^(−0.4,0.6)(𝑥)+0.48556046784167101822183413097838𝑃1^(−0.4,0.6)(𝑥)−0.018735918702094560665272214650799𝑃2^(−0.4,0.6)(𝑥)−0.021911869735090742971371812015998𝑃3^(−0.4,0.6)(𝑥).
𝛼=0.6,; 𝛽=0.6	𝑦=+0.00000000000000000185396073409571348071696317294𝑃0^(0.6,0.6)(𝑥)+0.93795482243803032015459053856673𝑃1^(0.6,0.6)(𝑥)+0.0000000000000000059326745972604669042025846148469𝑃2^(0.6,0.6)(𝑥)−0.078409581597779066879404197800853𝑃3^(0.6,0.6)(𝑥).
𝛼=2,; 𝛽=2	𝑦=+0.000000000000000002334262949979475861874127912143𝑃0^(2,2)(𝑥)+0.97023755744312467875938569010755𝑃1^(2,2)(𝑥)+0.00000000000000001400557769987685517124476747286𝑃2^(2,2)(𝑥)−0.10421967857002249036265594452531𝑃3^(2,2)(𝑥).