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International Journal of Computer Mathematics Volume 87, 2010 - Issue 1
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Section B

Some iterative methods for solving nonlinear equations using homotopy perturbation method

Muhammad Aslam Noor Mathematics Department, COMSATS Institute of Information Technology, Islamabad, PakistanCorrespondence[email protected]
Pages 141-149 | Received 10 Jan 2008, Accepted 28 Jan 2008, Published online: 22 Aug 2008

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Muhammad Aslam Noor, Khalida Inayat Noor, Sundas Khan & Muhammad Waseem. (2013) Modified homotopy perturbation method for solving system of linear equations. Journal of the Association of Arab Universities for Basic and Applied Sciences 13:1, pages 35-37.
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Articles from other publishers (31)

Muath Awadalla, Sania Qureshi, Amanullah Soomro & Kinda Abuasbeh. (2023) A Novel Three-Step Numerical Solver for Physical Models under Fractal Behavior. Symmetry 15:2, pages 330.
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Muqadssa Shahzadi. (2022) Some Approximate Schemes for Solving Nonlinear Equations. Earthline Journal of Mathematical Sciences, pages 79-91.
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O. Ababneh. (2022) New Iterative Methods for Solving Nonlinear Equations and Their Basins of Attraction. WSEAS TRANSACTIONS ON MATHEMATICS 21, pages 9-16.
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Asifa Tassaddiq, Sania Qureshi, Amanullah Soomro, Evren Hincal, Dumitru Baleanu & Asif Ali Shaikh. (2021) A New Three-Step Root-Finding Numerical Method and Its Fractal Global Behavior. Fractal and Fractional 5:4, pages 204.
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Feng Gao & Chunmei Chi. (2020) Pade Method for Construction of Numerical Algorithms for Fractional Initial Value Problem. Journal of Mathematics 2020, pages 1-7.
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Muhammad Shoaib Arif, Yasir Nawaz, Mairaj Bibi, Rabia Fayyaz & Mehvish Naz. (2019) A modification of He’s variational approach using the least square method to nonlinear oscillators. Journal of Low Frequency Noise, Vibration and Active Control 38:3-4, pages 996-1007.
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Wenxuan Kuang, Jun Wang, Chongxing Huang, Lixin Lu, De Gao, Zhiwei Wang & Changfeng Ge. (2019) Homotopy perturbation method with an auxiliary term for the optimal design of a tangent nonlinear packaging system. Journal of Low Frequency Noise, Vibration and Active Control 38:3-4, pages 1075-1080.
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Syed Ahmed Pasha, Yasir Nawaz & Muhammad Shoaib Arif. (2018) The modified homotopy perturbation method with an auxiliary term for the nonlinear oscillator with discontinuity. Journal of Low Frequency Noise, Vibration and Active Control 38:3-4, pages 1363-1373.
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M. Salai Mathi Selvi & L. Rajendran. (2019) Application of modified wavelet and homotopy perturbation methods to nonlinear oscillation problems. Applied Mathematics and Nonlinear Sciences 4:2, pages 351-364.
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Azar Shabani, Alireza Fatehi, FAhimeh Soltanian & Reza Jamilnia. (2019) Design of nonlinear continuous time predictive controller by solving the differential-algebraic equations with boundary conditions using homotopy perturbation method. Journal of Control 12:4, pages 1-14.
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Jalil Manafian & Cevat Teymuri sindi. (2018) An optimal homotopy asymptotic method applied to the nonlinear thin film flow problems. International Journal of Numerical Methods for Heat & Fluid Flow 28:12, pages 2816-2841.
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Ioannis K. Argyros, P. Jidesh & Santhosh George. (2015) Ball Convergence for Second Derivative Free Methods in Banach Space. International Journal of Applied and Computational Mathematics 3:2, pages 713-720.
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Uswah Qasim, Zulifqar Ali, Fayyaz Ahmad, Stefano Serra-Capizzano, Malik Zaka Ullah & Mir Asma. (2016) Constructing Frozen Jacobian Iterative Methods for Solving Systems of Nonlinear Equations, Associated with ODEs and PDEs Using the Homotopy Method. Algorithms 9:1, pages 18.
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Muhammad Waseem, Muhammad Aslam Noor & Khalida Inayat Noor. (2016) Efficient method for solving a system of nonlinear equations. Applied Mathematics and Computation 275, pages 134-146.
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Osama Y. Ababneh. (2016) New Fourth Order Iterative Methods Second Derivative Free. Journal of Applied Mathematics and Physics 04:03, pages 519-523.
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Muhammad Aslam Noor, Muhammad Waseem & Khalida Inayat Noor. (2015) New iterative technique for solving a system of nonlinear equations. Applied Mathematics and Computation 271, pages 446-466.
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H. Moosaei, S. Ketabchi, M.A. Noor, J. Iqbal & V. Hooshyarbakhsh. (2015) Some techniques for solving absolute value equations. Applied Mathematics and Computation 268, pages 696-705.
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Muhammad Aslam Noor, Muhammad Waseem, Khalida Inayat Noor & Muhammad Aamir Ali. (2015) New iterative technique for solving nonlinear equations. Applied Mathematics and Computation 265, pages 1115-1125.
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Muhammad Asif Zahoor Raja, Zulqurnain Sabir, Nasir Mehmood, Eman S. Al-Aidarous & Junaid Ali Khan. (2014) Design of stochastic solvers based on genetic algorithms for solving nonlinear equations. Neural Computing and Applications 26:1, pages 1-23.
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H. Saberi Najafi & S.A. Edalatpanah. (2014) Homotopy perturbation method for linear programming problems. Applied Mathematical Modelling 38:5-6, pages 1607-1611.
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Manoj Kumar, Akhilesh Kumar Singh & Akanksha Srivastava. (2013) Various Newton-type iterative methods for solving nonlinear equations. Journal of the Egyptian Mathematical Society 21:3, pages 334-339.
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Muhammad Aslam Noor, Muhammad Waseem, Khalida Inayat Noor & Eisa Al-Said. (2012) Variational iteration technique for solving a system of nonlinear equations. Optimization Letters 7:5, pages 991-1007.
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Xiang Hong, Jun Wang & Li-xin Lu. (2013) Application of Homotopy Perturbation Method with an Auxiliary Term for Nonlinear Dropping Equations Arisen in Polymer Packaging System. Mathematical Problems in Engineering 2013, pages 1-5.
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Muhammad Aslam Noor & Waseem Asghar Khan. (2012) New iterative methods for solving nonlinear equation by using homotopy perturbation method. Applied Mathematics and Computation 219:8, pages 3565-3574.
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Ji-Huan He. (2012) Homotopy Perturbation Method with an Auxiliary Term. Abstract and Applied Analysis 2012, pages 1-7.
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Yanqin Liu. (2012) Approximate Solutions of Fractional Nonlinear Equations Using Homotopy Perturbation Transformation Method. Abstract and Applied Analysis 2012, pages 1-14.
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Yanqin Liu. (2012) Variational Homotopy Perturbation Method for Solving Fractional Initial Boundary Value Problems. Abstract and Applied Analysis 2012, pages 1-10.
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Muhammad Aslam Noor, Khalida Inayat Noor, Zhenyu Huang & Eisa Al-Said. (2012) Implicit Schemes for Solving Extended General Nonconvex Variational Inequalities. Journal of Applied Mathematics 2012, pages 1-10.
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M. Rafiullah. (2011) A fifth-order iterative method for solving nonlinear equations. Numerical Analysis and Applications 4:3, pages 239-243.
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Deniz Ağırseven & Turgut Öziş. (2010) An analytical study for Fisher type equations by using homotopy perturbation method. Computers & Mathematics with Applications 60:3, pages 602-609.
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M.A. El-Gebeily, Donal O’Regan & J.J. Nieto. (2010) A monotone iterative technique for stationary and time dependent problems in Banach spaces. Journal of Computational and Applied Mathematics 233:9, pages 2395-2404.
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