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Mathematical Sciences Letters
An International Journal


Volumes > Vol. 1 > No. 1


Numerical Solution of Linear HPDEs Via Bernoulli Operational Matrix of Differentiation and Comparison with Taylor Matrix Method

PP: 61-70
EmranTohidi, Mohammad Shirazian,
In this paper a new matrix approach for solving linear hyperbolic partial differential equations (HPDEs) is presented. The method is based on the Bernoulli expansion of two-variable functions, which consists of the matrix representation of expressions in the considered HPDE. Also, a new operational matrix of differentiation is introduced, which consists of nonzero elements under its diagonal, meanwhile the operational matrix of differentiation of other polynomial bases (such as Chebyshev, Legendre, etc.) is a strictly (upper or lower) triangular matrix. In the proposed method, HPDE together with the initial and boundary conditions are transformed into the matrix equations, which corresponds to a system of linear algebraic equations with the unknown Bernoulli coefficients. Combining these matrix equations and then solving the system yields the Bernoulli coefficients of the approximated solution. Illustrative examples are included to demonstrate the validity and applicability of the technique. All of computations are performed on a PC using several programs written in MATLAB 7.12.0.

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