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International Journal of Computer Mathematics Volume 79, 2002 - Issue 9
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Original Articles

A Taylor Collocation Method for the Solution of Linear Integro-Differential Equations

Aysen Karamete Department of Computer Education and Instructional Technology, Faculty of Education, Balikesir University, Balikesir, Turkey; Department of Mathematics, Faculty of Education, Balikesir University, Balikesir, 10100, Turkey
&
Mehmet Sezer Department of Mathematics, Faculty of Education, okuz Eylül University, İzmir, Turkey
Pages 987-1000 | Published online: 15 Sep 2010

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H. O. Bakodah, M. Al-Mazmumy & S. O. Almuhalbedi. (2019) Solving system of integro differential equations using discrete adomian decomposition method. Journal of Taibah University for Science 13:1, pages 805-812.
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Gül Gözde Biçer, Yalçın Öztürk & Mustafa Gülsu. (2018) Numerical approach for solving linear Fredholm integro-differential equation with piecewise intervals by Bernoulli polynomials. International Journal of Computer Mathematics 95:10, pages 2100-2111.
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M. S. Hashemi, E. Darvishi & M. Inc. (2018) A geometric numerical integration method for solving the Volterra integro-differential equations. International Journal of Computer Mathematics 95:8, pages 1654-1665.
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Berna Bülbül & Mehmet Sezer. (2011) Taylor polynomial solution of hyperbolic type partial differential equations with constant coefficients. International Journal of Computer Mathematics 88:3, pages 533-544.
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Ayşegül Akyüz-Daşcioğlu & Mehmet Sezer. (2007) A Taylor polynomial approach for solving high-order linear Fredholm integro-differential equations in the most general form. International Journal of Computer Mathematics 84:4, pages 527-539.
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Xian-Fang Li & Min Fang. (2006) Modified method for determining an approximate solution of the Fredholm–Volterra integral equations by Taylor’s expansion. International Journal of Computer Mathematics 83:8-9, pages 637-649.
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Mustafa Gülsu & Mehmet Sezer. (2006) Taylor collocation method for solution of systems of high-order linear Fredholm–Volterra integro-differential equations. International Journal of Computer Mathematics 83:4, pages 429-448.
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Mehmet Sezer, Ayşen Karamete & Mustafa Gülsu. (2005) Taylor polynomial solutions of systems of linear differential equations with variable coefficients. International Journal of Computer Mathematics 82:6, pages 755-764.
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Mehmet Sezer & Mustafa Gülsu. (2005) Polynomial solution of the most general linear Fredholm integrodifferential–difference equations by means of Taylor matrix method. Complex Variables, Theory and Application: An International Journal 50:5, pages 367-382.
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Cheima Khennaoui, Azzeddine Bellour & Hafida Laib. (2023) Taylor collocation method for solving two‐dimensional partial Volterra integro‐differential equations. Mathematical Methods in the Applied Sciences 46:12, pages 12735-12758.
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Momna Tariq, Mujeeb ur Rehman & Umer Saeed. (2022) A generalized Taylor operational matrix method for ψ ‐fractional differential equations . Mathematical Methods in the Applied Sciences 46:4, pages 4705-4727.
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Shaheed N. Huseen & Rawan A. Shlaka. Numerical solutions of Fredholm integral and integro-differential equations. Numerical solutions of Fredholm integral and integro-differential equations.
O. A. Taiwo, M. O. Etuk, E. Nwaeze & M. O. Ogunniran. (2022) Enhanced moving least square method for the solution of volterra integro-differential equation: an interpolating polynomial. Journal of the Egyptian Mathematical Society 30:1.
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Şuayip Yüzbaşı & Gamze Yıldırım. (2022) A collocation method to solve the parabolic-type partial integro-differential equations via Pell–Lucas polynomials. Applied Mathematics and Computation 421, pages 126956.
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Ekhlass S. Al-Rawi & Merna A. Samarchi. (2022) On the Use of Elzaki Decomposition Method for Solving Higher-Order Integro-Differential Equations. International Journal of Mathematics and Mathematical Sciences 2022, pages 1-8.
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Elayaraja Aruchunan, Mohana Sundaram Muthuvalu, Zailan Siri, Sachin Sharma Ashok Kumar, Jumat Sulaiman, Jackel Vui Lung Chew & Majid Khan Majahar Ali. 2022. Towards Intelligent Systems Modeling and Simulation. Towards Intelligent Systems Modeling and Simulation 413 430 .
Salwa A. Mohamed, Norhan A. Mohamed & Sarah I. Abo‐Hashem. (2021) A novel differential‐integral quadrature method for the solution of nonlinear integro‐differential equations. Mathematical Methods in the Applied Sciences 44:18, pages 13945-13967.
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H. Bin Jebreen. (2020) On the Multiwavelets Galerkin Solution of the Volterra–Fredholm Integral Equations by an Efficient Algorithm. Journal of Mathematics 2020, pages 1-10.
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Hong Du & Zhong Chen. (2020) A new reproducing kernel method with higher convergence order for solving a Volterra–Fredholm integral equation. Applied Mathematics Letters 102, pages 106117.
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Yousef Jafarzadeh & Reza Ezzati. (2019) A new method for the solution of Volterra-Fredholm integro-differential equations. Tbilisi Mathematical Journal 12:2.
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Hassan Hamad AL-Nasrawy, Abdul Khaleq O. Al-Jubory & Kasim Abbas Hussaina. (2019) An Efficient Algorithm for Solving Integro-Differential Equation. Journal of Southwest Jiaotong University 54:6.
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S. Narayanamoorthy & S. Mathankumar. (2018) Variational iterative method: an appropriate numerical scheme for solving system of linear Volterra fuzzy integro-differential equations. Advances in Difference Equations 2018:1.
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Yousef Jafarzadeh & Bagher Keramati. (2018) Numerical method for a system of integro-differential equations and convergence analysis by Taylor collocation. Ain Shams Engineering Journal 9:4, pages 1433-1438.
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M. H. Daliri Birjandi, J. Saberi-Nadjafi & A. Ghorbani. (2018) An Efficient Numerical Method for a Class of Nonlinear Volterra Integro-Differential Equations. Journal of Applied Mathematics 2018, pages 1-7.
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Saeid Abbasbandy. (2017) A new class of polynomial functions equipped with a parameter. Mathematical Sciences 11:2, pages 127-130.
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S.Yu. Reutskiy. (2016) The backward substitution method for multipoint problems with linear Volterra–Fredholm integro-differential equations of the neutral type. Journal of Computational and Applied Mathematics 296, pages 724-738.
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Faisal M. Mukhtar. (2016) Generalized Taylor polynomials for axisymmetric plates and shells. Applied Mathematics and Computation 276, pages 182-199.
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Suayip Yüzbasi, Emrah Gök & Mehmet Sezer. (2016) A numerical method for solving systems of higher order linear functional differential equations. Open Physics 14:1, pages 15-25.
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Şuayip Yüzbaşı. (2016) A collocation method based on Bernstein polynomials to solve nonlinear Fredholm–Volterra integro-differential equations. Applied Mathematics and Computation 273, pages 142-154.
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Keyan Wang & Qisheng Wang. (2014) Taylor collocation method and convergence analysis for the Volterra–Fredholm integral equations. Journal of Computational and Applied Mathematics 260, pages 294-300.
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Xiaomin Wang. (2014) A New Wavelet Method for Solving a Class of Nonlinear Volterra-Fredholm Integral Equations. Abstract and Applied Analysis 2014, pages 1-6.
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Keyan Wang & Qisheng Wang. (2013) Lagrange collocation method for solving Volterra–Fredholm integral equations. Applied Mathematics and Computation 219:21, pages 10434-10440.
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Şuayip Yüzbaşı, Mehmet Sezer & Bayram Kemancı. (2013) Numerical solutions of integro-differential equations and application of a population model with an improved Legendre method. Applied Mathematical Modelling 37:4, pages 2086-2101.
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Z. Pashazadeh Atabakan, A. Kazemi Nasab, A. Kılıçman & Zainidin K. Eshkuvatov. (2013) Numerical Solution of Nonlinear Fredholm Integro-Differential Equations Using Spectral Homotopy Analysis Method. Mathematical Problems in Engineering 2013, pages 1-9.
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Yalçın Öztürk, Ayşe Anapalı, Mustafa Gülsu & Mehmet Sezer. (2013) A Collocation Method for Solving Fractional Riccati Differential Equation. Journal of Applied Mathematics 2013, pages 1-8.
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F. Ghomanjani, A. Kılıçman & S. Effati. (2013) Numerical Solution for IVP in Volterra Type Linear Integrodifferential Equations System. Abstract and Applied Analysis 2013, pages 1-4.
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Salih Yalçınbaş & Tuğçe Akkaya. (2012) A numerical approach for solving linear integro-differential-difference equations with Boubaker polynomial bases. Ain Shams Engineering Journal 3:2, pages 153-161.
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Isabella Cravero, Giovanna Pittaluga & Laura Sacripante. (2011) An algorithm for solving linear Volterra integro-differential equations. Numerical Algorithms 60:1, pages 101-114.
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Z. Pashazadeh Atabakan, A. Kılıçman & A. Kazemi Nasab. (2012) On Spectral Homotopy Analysis Method for Solving Linear Volterra and Fredholm Integrodifferential Equations. Abstract and Applied Analysis 2012, pages 1-16.
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Nilay Akgönüllü, Niyazi Şahin & Mehmet Sezer. (2011) A Hermite collocation method for the approximate solutions of high-order linear Fredholm integro-differential equations. Numerical Methods for Partial Differential Equations 27:6, pages 1707-1721.
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Nurcan Baykus & Mehmet Sezer. (2011) Solution of high-order linear Fredholm integro-differential equations with piecewise intervals. Numerical Methods for Partial Differential Equations 27:5, pages 1327-1339.
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Mehmet Sezer, Mustafa Gülsu & Bekir Tanay. (2011) Rational Chebyshev collocation method for solving higher-order linear ordinary differential equations. Numerical Methods for Partial Differential Equations 27:5, pages 1130-1142.
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Ş. Yüzbaşi, N. Şahin & M. Gülsu. (2011) A collocation approach for solving a class of complex differential equations in elliptic domains. Journal of Numerical Mathematics 19:3.
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Mehmet Sezer, Bekir Tanay & Mustafa Gülsu. (2010) Numerical solution of a class of complex differential equations by the Taylor collocation method in elliptic domains. Numerical Methods for Partial Differential Equations 26:5, pages 1191-1205.
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Mustafa Gülsu, Yalçın Öztürk & Mehmet Sezer. (2010) A new collocation method for solution of mixed linear integro-differential-difference equations. Applied Mathematics and Computation 216:7, pages 2183-2198.
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Yücel Çenesiz, Yıldıray Keskin & Aydın Kurnaz. (2010) The solution of the Bagley–Torvik equation with the generalized Taylor collocation method. Journal of the Franklin Institute 347:2, pages 452-466.
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Elçin Yusufoğlu (Agadjanov). (2009) Numerical solving initial value problem for Fredholm type linear integro-differential equation system. Journal of the Franklin Institute 346:6, pages 636-649.
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Salih Yalçinbaş, Mehmet Sezer & Hüseyin Hilmi Sorkun. (2009) Legendre polynomial solutions of high-order linear Fredholm integro-differential equations. Applied Mathematics and Computation 210:2, pages 334-349.
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Nurcan Kurt & Mehmet Sezer. (2008) Polynomial solution of high-order linear Fredholm integro-differential equations with constant coefficients. Journal of the Franklin Institute 345:8, pages 839-850.
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Mehmet Sezer & Mustafa Gülsu. (2007) Polynomial solution of the most general linear Fredholm–Volterra integrodifferential-difference equations by means of Taylor collocation method. Applied Mathematics and Computation 185:1, pages 646-657.
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Mustafa Gülsu & Mehmet Sezer. (2006) Approximations to the solution of linear Fredholm integrodifferential–difference equation of high order. Journal of the Franklin Institute 343:7, pages 720-737.
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Mehmet Sezer, Mustafa Gülsu & Bekir Tanay. (2006) A Taylor collocation method for the numerical solution of complex differential equations with mixed conditions in elliptic domains. Applied Mathematics and Computation 182:1, pages 498-508.
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Ayşegül Akyüz-Daşcıogˇlu. (2006) A Chebyshev polynomial approach for linear Fredholm–Volterra integro-differential equations in the most general form. Applied Mathematics and Computation 181:1, pages 103-112.
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Mustafa Gülsu, Mehmet Sezer & Bekir Tanay. (2006) A matrix method for solving high-order linear difference equations with mixed argument using hybrid legendre and taylor polynomials. Journal of the Franklin Institute 343:6, pages 647-659.
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Mehmet Sezer & Mustafa Gülsu. (2006) Approximate solution of complex differential equations for a rectangular domain with Taylor collocation method. Applied Mathematics and Computation 177:2, pages 844-851.
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Jichao Zhao & Robert M. Corless. (2006) Compact finite difference method for integro-differential equations. Applied Mathematics and Computation 177:1, pages 271-288.
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Salih Yalçinbaş & Mehmet Sezer. (2006) A Taylor collocation method for the approximate solution of general linear Fredholm–Volterra integro-difference equations with mixed argument. Applied Mathematics and Computation 175:1, pages 675-690.
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Mustafa Gülsu, Mehmet Sezer & Zekeriya Güney. (2006) Approximate solution of general high-order linear nonhomogeneous difference equations by means of Taylor collocation method. Applied Mathematics and Computation 173:2, pages 683-693.
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Inga Parts, Arvet Pedas & Enn Tamme. (2005) Piecewise Polynomial Collocation for Fredholm Integro-Differential Equations with Weakly Singular Kernels. SIAM Journal on Numerical Analysis 43:5, pages 1897-1911.
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