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Numerical solution of high order linear complex differential equations via complex operational matrix method

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Abstract

In this work, a numerical method based on a complex operational matrix is utilized to solve high order linear complex differential equations under mixed initial conditions. For this aim, we introduce orthonormal Bernstein polynomials (OBPs), and we obtain their complex operational matrix of differentiation. The main advantage of the proposed method is that by using this method complex differential equations reduce to a linear system of algebraic equations which can be solved by using an appropriate iterative method. To, some results concerning the error analysis associated with the present method are discussed. Finally, we give some numerical examples to reveal accuracy and efficiency of the proposed method. Also, the numerical results obtained by this method are compared with numerical results achieved from other existing methods.

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Acknowledgements

The authors would like to express our very great appreciation to editor and anonymous reviewers for their valuable comments and constructive suggestions which have helped to improve the quality and presentation of this paper.

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Authors and Affiliations

  1. Faculty of Mathematical Sciences and Statistics, Malayer University, P. O. Box 65719-95863, Malayer, Iran

    Farshid Mirzaee, Nasrin Samadyar & Sahar Alipour

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  1. Farshid Mirzaee
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  2. Nasrin Samadyar
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  3. Sahar Alipour
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Correspondence to Farshid Mirzaee.

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Mirzaee, F., Samadyar, N. & Alipour, S. Numerical solution of high order linear complex differential equations via complex operational matrix method. SeMA 76, 1–13 (2019). https://doi.org/10.1007/s40324-018-0151-7

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  • DOI: https://doi.org/10.1007/s40324-018-0151-7

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