The numerical solution of bioheat equation based on shifted Legendre polynomial

[1] M. Abdelkawy, E. Ahmed and P. Sanchez, A method based on Legendre Pseudo-Spectral Approximations for Solving Inverse Problems of Parabolic Types Equations, Mathematical Sciences Letters An International Journal, 1 (2011) 81-90.
[2] F. Ahmad, A. Alomari, A. Bataineh, J. Sulaiman and I. Hashim, On the approximate solutions of systems of ODEs by Legendre operational matrix of differentiation, Italian Journal of Pure and Applied Mathematics, 36 (2016) 483-494.
[3] M. Alshbool , A. Bataineh , I. Hashim and O. Isik, Approximate solutions of singular differential equations with estimation error by using Bernstein polynomials, International Journal of Pure and Applied Mathematics, 1 (2015) 109-125.
[4] A. Bah¸si and S. Yal¸cinbas, A new algorithm for the numerical solution of telegraph equations by using Fibonacci polynomials, Mathematics and Computational Applications, 15 (2016) 1-12.
[5] A. Bhrawy and A. Alof, A Jacobi-Gauss collocation method for solving nonlinear Lane-Emden type equations, Commun Nonlinear Sci Numer Simulat, 17 (2012) 62-70.
[6] M. Dehghan and M. Sabouri, A spectral element method for solving the Pennes bioheat transfer equation by using triangular and quadrilateral elements, Applied Mathematical Modelling, 36 (2012) 6031-6049.
[7] L. Ferr´as, N. Ford, M. Morgado, J. Nobrega and M. Rebelo, Fractional Penne´s bioheat equation: Theoretical and numerical studies, Fractional Calculus and Applied Analysis, 4 (2015) 1080-1106.
[8] A. G¨uner and S. Yal¸cinbas, Legendre collocation method for solving nonlinear differential equations, Mathematical and Computational Applications, 3 (2013) 521-530.
[9] B. G¨urb¨uz and M. Sezer, Laguerre Polynomial Approach for Solving Nonlinear Klein-Gordon Equations, Malaysian Journal of Mathematical Sciences, 2 (2017) 191-203.
[10] M. Heydari, M. Hooshmandasl and F. Ghaini, A new approach of the Chebyshev wavelets method for partial differential equations with boundary conditions of the telegraph type, Applied Mathematical Modelling, 38 (2014) 1597-1606.
[11] M. Idrees and P. Bracken, Solutions of differential equations in a Bernstein polynomial basis, Journal of Computational and Applied Mathematics, 205 (2007) 272-280.
[12] S. Khan and I. Ali, Application of Legendre spectral-collocation method to delay differential and stochastic delay differential equation , AIP Advances, 8 (2018) 1-10.
[13] H. Pennes, Analysis of tissue and arterial blood temperature in the resting forearm, Journal of applied physiology, 1 (1984) 93-122.
[14] A. Saadatmandi and M. Razzaghi, A Tau method approach for the diffusion equation with nonlocal boundary conditions, International Journal of Computer Mathematics, 11 (2004) 1427-1432.
[15] E.Tohidi, A. Bhrawy and K.Erfani, A collocation method based on Bernoulli operational matrix for numerical solution of generalized pantograph equation, Applied Mathematical Modelling, 6 (2013) 4283-4294.
[16] E. Tohidi, Legendre approximation for solving linear HPDEs and comparison with Taylor and Bernoulli matrix methods, Applied Mathematics, 3 (2012) 410-416.
[17] S. Yal¸cibas, M. Aynig¨ul and M. Sezer, A collocation method using Hermite polynomials for approximate solution of pantograph equations, Journal of the Franklin Institute, 348 (2011) 1128-1139.
[18] S. Yousefi, Legendre scaling function for solving generalized Emden-Fowler equations, International Journal of Information and Systems Sciences, 2 (2007) 243-250.