Table 6 Comparison solution by MDTM, FDM, and shooting method with Nu and HPM [35] for θ (η) when \({ }\varphi\) = 0.01, δ = 1, P = 0, Ha = 0, \(\frac{1}{{R_{d} }}\) = 0, Ec = 1, Pr = 6.2, and \(\alpha\) = 0
η | Present θ (η) | θ (η) [35] | |||
|---|---|---|---|---|---|
MDTM | FDM | Shooting method | Nu | HPM | |
− 1 | 0.500000000000000 | 0.500000000000000 | 0.500612300000000 | 0.5 | 0.5 |
− 0.8 | 0.4048517213003998 | 0.404741915710620 | 0.404681040960000 | 0.404852 | 0.404687 |
− 0.6 | 0.3075705040841343 | 0.308430072374435 | 0.308052719840000 | 0.307571 | 0.307541 |
− 0.4 | 0.2100694862476117 | 0.211064469991446 | 0.210698745920000 | 0.210070 | 0.210225 |
− 0.2 | 0.1121566516441399 | 0.112645108561653 | 0.112462917600000 | 0.112157 | 0.112397 |
0 | 0.0130337276413045 | 0.013171988085055 | 0.013145000000000 | 0.013034 | 0.013246 |
0.2 | − 0.0877464857138474 | − 0.087354891438347 | − 0.08741569744000 | − 8.77e−02 | − 8.76e−02 |
0.4 | − 0.1899083279925779 | − 0.188935530008554 | − 0.18925674336000 | − 0.189907 | − 0.189774 |
0.6 | − 0.2926661222188964 | − 0.291569927625565 | − 0.29220900688000 | − 0.292665 | − 0.292458 |
0.8 | − 0.3955710872738615 | − 0.395258084289380 | − 0.39581308000000 | − 0.395570 | − 0.395312 |
1 | − 0.5000000187397369 | − 0.500000000000000 | − 0.49923570000000 | − 0.5 | − 0.5 |