AUTHORS: Jacob Manale

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ABSTRACT: We determine the group invariant solutions of the nonlinear heat equation though the linear case, using a relation that exists between the two. This is not new, but there has always been those solutions that proved difficult to evaluate through existing symmetry techniques, for both linear and nonlinear cases. We introduce what we call modified Lie symmetries to address these difficulties

KEYWORDS: Group method; Heat diffusion; Nonlinear problems; Modified symmetries

REFERENCES:

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[12]. Gholinia, M., Gholinia, S., Akbari, N., Ganji, D.D.: Analytical and numerical study to nonlinear heat transfer equation in strait fin. Innovative Energy and Research. 5(2), 1—6 (2016) 13]. Manale, J.M.: Introducing smart symmetries with application to gravity related radiation. Int. J. Math. and Com. 1, 40—47 (2016)

[14]. Manale, J.M.: On a Financial Engineering Formula for European Options, Int. J. Appl. Eng. Res., 11, 7758--7766 (2016)

[15]. Manale, J.M.: Group analysis of differential equations: A new type of Lie symmetries, Int. J. Appl. Eng. Res., 13, 12029-12039 (2018)