On the differential transform method of solving boundary eigenvalue problems: An illustration
boundary eigenvalue problem; DarcyBrinkman convection; differential transform method; general boundary conditions; porous medium
The differential transform method (DTM) is a simple technique based on the Taylor series. Applying the DTM, a given linear boundary eigenvalue problem (BEVP) involving ordinary differential equations is converted into a recurrence relation or a system of recurrence relations for the Taylor coefficients. This ultimately leads to the solution of the problem in the form of an infinite power series with an appropriate region of convergence. The present paper aims to apply the DTM in solving a BEVP arising from the DarcyBrinkman convection in a rectangular box subject to general boundary conditions whose vertical sidewalls are assumed to be impermeable and adiabatic. The non-dimensional temperature difference between the plates represented by the DarcyRayleigh number, the eigenvalue of the problem, is obtained as a function of the width of the Bard cell ((Formula presented.) : b is the horizontal wave number) and other parameters using the DTM. The work includes investigation on the convergence of the series solution. The solution by the DTM is compared with that obtained by the MATLAB bvp4c routine and excellent agreement is found thereby establishing the accuracy of theDTM. 2020 Wiley-VCH GmbH
Narayana M.; Shekar M.; Siddheshwar P.G.; Anuraj N.V.
ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, Vol-101, No. 5
https://doi.org/10.1002/zamm.202000114 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85097429711&doi=10.1002%2fzamm.202000114&partnerID=40&md5=a62ced86e14b1279f43d6564b1962caa
Narayana M., Department of Mathematics, The University of the West Indies, Mona Campus, Kingston 7, St. Andrew, Jamaica; Shekar M., Department of Mathematics and Statistics, M. S. Ramaiah University of Applied Sciences, Peenya Campus, Bengaluru, 560058, Karnataka, India; Siddheshwar P.G., Department of Mathematics, CHRIST(Deemed to be University), Hosur Road, Bengaluru, 560029, Karnataka, India; Anuraj N.V., Department of Mathematics and Statistics, M. S. Ramaiah University of Applied Sciences, Peenya Campus, Bengaluru, 560058, Karnataka, India