Journal: Computational and Applied Mathematics

Article Title: Monic Chebyshev pseudospectral differentiation matrices for higher-order IVPs and BVPs: applications to certain types of real-life problems

doi: 10.1007/s40314-022-01940-0

Figure Lengend Snippet: The point wise AE for Example 7 using 11 points

Article Snippet: On the other hand, the bvp5c Matlab function got “5.5e \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-$$\end{document} - 12” using 7 points.

Techniques:

Journal: Computational and Applied Mathematics

Article Title: Monic Chebyshev pseudospectral differentiation matrices for higher-order IVPs and BVPs: applications to certain types of real-life problems

doi: 10.1007/s40314-022-01940-0

Figure Lengend Snippet: The MAE for Example 8

Article Snippet: On the other hand, the bvp5c Matlab function got “5.5e \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-$$\end{document} - 12” using 7 points.

Techniques:

Journal: Computational and Applied Mathematics

Article Title: Monic Chebyshev pseudospectral differentiation matrices for higher-order IVPs and BVPs: applications to certain types of real-life problems

doi: 10.1007/s40314-022-01940-0

Figure Lengend Snippet: The point wise AE for Example 4

Article Snippet: On the other hand, the bvp5c Matlab function got “5.5e \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-$$\end{document} - 12” using 7 points.

Techniques:

Journal: Scientific Reports

Article Title: Critical analysis for nonlinear oscillations by least square HPM

doi: 10.1038/s41598-024-51706-3

Figure Lengend Snippet: Comparison of HPM, LSHPM, AGM and bvp5c results when \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k = 100$$\end{document} k = 100 , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g = 9.8$$\end{document} g = 9.8 , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_{1} = 5,$$\end{document} m 1 = 5 , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_{2} = 1$$\end{document} m 2 = 1 , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L = 1$$\end{document} L = 1 , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A = \frac{\pi }{6}$$\end{document} A = π 6 .

Article Snippet: In this manuscript, we use the newly developed LSHPM and MATLAB builtin functiobn bvp5c to unfold the problem .

Techniques: Comparison

Journal: Scientific Reports

Article Title: Critical analysis for nonlinear oscillations by least square HPM

doi: 10.1038/s41598-024-51706-3

Figure Lengend Snippet: Comparison of HPM, LSHPM, AGM and bvp5c results when \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A = 0.25$$\end{document} A = 0.25 , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Lambda = \frac{\pi }{3}$$\end{document} Λ = π 3 .

Article Snippet: In this manuscript, we use the newly developed LSHPM and MATLAB builtin functiobn bvp5c to unfold the problem .

Techniques: Comparison

Journal: Scientific Reports

Article Title: Numerical analysis of Casson nanofluid three-dimensional flow over a rotating frame exposed to a prescribed heat flux with viscous heating

doi: 10.1038/s41598-022-08211-2

Figure Lengend Snippet: Comparison of − θ' (0) values with of Khan and Pop 38 and Gorla and Sidawi 46 when \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Nb=Nt=\lambda ={\beta }_{E}=\phi =0$$\end{document} N b = N t = λ = β E = ϕ = 0 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Bi=\text{10,000}$$\end{document} B i = 10,000 .

Article Snippet: The system first-order governing equations are solved using the MATLAB—bvp5c routine (see Ref. ).

Techniques: Comparison