Generalized Bessel quasilinearization technique applied to Bratu and Lane-Emden-type equations of arbitrary order

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dc.contributor.authorIzadi, Mohammad
dc.contributor.authorSrivastava, H.M.
dc.date.accessioned2022-11-13T15:06:11Z
dc.date.available2022-11-13T15:06:11Z
dc.date.copyright2021en_US
dc.date.issued2021
dc.description.abstractThe ultimate goal of this study is to develop a numerically effective approximation technique to acquire numerical solutions of the integer and fractional-order Bratu and the singular Lane–Emden-type problems especially with exponential nonlinearity. Both the initial and boundary conditions were considered and the fractional derivative being considered in the Liouville–Caputo sense. In the direct approach, the generalized Bessel matrix method based on collocation points was utilized to convert the model problems into a nonlinear fundamental matrix equation. Then, the technique of quasilinearization was employed to tackle the nonlinearity that arose in our considered model problems. Consequently, the quasilinearization method was utilized to transform the original nonlinear problems into a sequence of linear equations, while the generalized Bessel collocation scheme was employed to solve the resulting linear equations iteratively. In particular, to convert the Neumann initial or boundary condition into a matrix form, a fast algorithm for computing the derivative of the basis functions is presented. The error analysis of the quasilinear approach is also discussed. The effectiveness of the present linearized approach is illustrated through several simulations with some test examples. Comparisons with existing well-known schemes revealed that the presented technique is an easy-to-implement method while being very effective and convenient for the nonlinear Bratu and Lane–Emden equations.en_US
dc.description.reviewstatusRevieweden_US
dc.description.scholarlevelFacultyen_US
dc.identifier.citationIzadi, M. & Srivastava, H. M. (2021). “Generalized Bessel quasilinearization technique applied to Bratu and Lane-Emden-type equations of arbitrary order.” Fractal and Fractional, 5(4), 179. https://doi.org/10.3390/fractalfract5040179en_US
dc.identifier.urihttps://doi.org/10.3390/fractalfract5040179
dc.identifier.urihttp://hdl.handle.net/1828/14464
dc.language.isoenen_US
dc.publisherFractal and Fractionalen_US
dc.subjectBessel functionsen_US
dc.subjectBratu's problemen_US
dc.subjectcollocation methoden_US
dc.subjecterror analysisen_US
dc.subjectLane-Emden equationen_US
dc.subjectLiouville-Caputo fractional derivativeen_US
dc.subjectquasilinearization techniqueen_US
dc.titleGeneralized Bessel quasilinearization technique applied to Bratu and Lane-Emden-type equations of arbitrary orderen_US
dc.typeArticleen_US

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