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Relevant bibliographies by topics / Volterra integro-differential equations

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Academic literature on the topic 'Volterra integro-differential equations'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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Journal articles on the topic "Volterra integro-differential equations"

1

Tarang, M. "STABILITY OF THE SPLINE COLLOCATION METHOD FOR SECOND ORDER VOLTERRA INTEGRO‐DIFFERENTIAL EQUATIONS." Mathematical Modelling and Analysis 9, no. 1 (2004): 79–90. http://dx.doi.org/10.3846/13926292.2004.9637243.

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Numerical stability of the spline collocation method for the 2nd order Volterra integro‐differential equation is investigated and connection between this theory and corresponding theory for the 1st order Volterra integro‐differential equation is established. Results of several numerical tests are presented. Straipsnyje nagrinejamas antros eiles Volteros integro‐diferencialiniu lygčiu splainu kolokaci‐jos metodo skaitinis stabilumas ir nustatytas ryšys tarp šios teorijos ir atitinkamos pirmos eiles Volterra integro‐diferencialiniu lygčiu teorijos. Pateikti keleto skaitiniu eksperimentu rezultat

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Butris, Raad Noori, and Noori R. Noori. "APPROXIMATE AND STABILITY SOLUTION FOR NON-LINEAR SYSTEM OF INTEGRODIFFERENTIAL EQUATIONS OF VOLTERRA TYPE WITH BOUNDARY CONDITIONS." IJISCS (International Journal of Information System and Computer Science) 7, no. 2 (2023): 124. http://dx.doi.org/10.56327/ijiscs.v7i2.1482.

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In this paper, we investigate the approximation and stability solutions of non-linear systems of integro-differential equations of Volterra type with boundary conditions, by using the numerical-analytic method which were introduced by Samoilenko. The study of such integro-differential equations leads to extend the results obtained by Butris for changing the system of non-linear integro- differential equations of Volterra type to the system of non-linear integro-differential equations of the Volterra type with boundary conditions. Theorems on a solutions are established under some necessary and

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3

D., Umar, and L. Bichi S. "On the Existence of Solutions of Multi-Term Fractional Order Volterra Integro-Differential Equations." International Journal of Mathematical Sciences and Optimization: Theory and Applications 10, no. 4 (2024): 99–113. https://doi.org/10.5281/zenodo.14710636.

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In this paper, the problem of multi-term fractional order Volterra integro-differential equations is considered. The multi-term fractional order derivative part of the multi-term fractional order Volterra integro-differential equations is converted to its equivalent integral equation and Schauder’s fixed point theorem is applied to establish the existence of solutions for the multi-term fractional order Volterra integro-differential equations under some mild conditions. Furthermore, examples were given to test the applicability of the proposed theorem.

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Qahremani, E., T. Allahviranloo, S. Abbasbandy, and N. Ahmady. "A study on the fuzzy parabolic Volterra partial integro-differential equations." Journal of Intelligent & Fuzzy Systems 40, no. 1 (2021): 1639–54. http://dx.doi.org/10.3233/jifs-201125.

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This paper is concerned with aspects of the analytical fuzzy solutions of the parabolic Volterra partial integro-differential equations under generalized Hukuhara partial differentiability and it consists of two parts. The first part of this paper deals with aspects of background knowledge in fuzzy mathematics, with emphasis on the generalized Hukuhara partial differentiability. The existence and uniqueness of the solutions of the fuzzy Volterra partial integro-differential equations by considering the type of [gH - p]-differentiability of solutions are proved in this part. The second part is

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Li, Yunfei, and Shoufu Li. "Classical Theory of Linear Multistep Methods for Volterra Functional Differential Equations." Discrete Dynamics in Nature and Society 2021 (March 11, 2021): 1–15. http://dx.doi.org/10.1155/2021/6633554.

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Based on the linear multistep methods for ordinary differential equations (ODEs) and the canonical interpolation theory that was presented by Shoufu Li who is exactly the second author of this paper, we propose the linear multistep methods for general Volterra functional differential equations (VFDEs) and build the classical stability, consistency, and convergence theories of the methods. The methods and theories presented in this paper are applicable to nonneutral, nonstiff, and nonlinear initial value problems in ODEs, Volterra delay differential equations (VDDEs), Volterra integro-different

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Yang, Ai-Min, Yang Han, Yu-Zhu Zhang, Li-Ting Wang, Di Zhang, and Xiao-Jun Yang. "On local fractional Volterra integro-differential equations in fractal steady heat transfer." Thermal Science 20, suppl. 3 (2016): 789–93. http://dx.doi.org/10.2298/tsci16s3789y.

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In this paper we address the inverse problems for the fractal steady heat transfer described by the local fractional linear and non-linear Volterra integro-differential equations. The Volterra integro-differential equations are presented for investigating the fractal heat-transfer.

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GIL', M. I. "POSITIVITY OF GREEN'S FUNCTIONS TO VOLTERRA INTEGRAL AND HIGHER ORDER INTEGRO-DIFFERENTIAL EQUATIONS." Analysis and Applications 07, no. 04 (2009): 405–18. http://dx.doi.org/10.1142/s0219530509001475.

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We consider Volterra integral equations and arbitrary order integro-differential equations. We establish positivity conditions and two-sided estimates for Green's functions. These results are then applied to obtain stability and positivity conditions for equations with nonlinear causal mappings (operators) and linear integro-differential parts. Such equations include differential, difference, differential-delay, integro-differential and other traditional equations.

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Kareem, Kabiru Oyeleye, Morufu Oyedunsi Olayiwola, and Muideen Odunayo Ogunniran. "Advances In Modification of Adomian Decomposition Method and Their Application to Integral Equations." Parrot: A Multi-Disciplinary Journal of the Federal College of Education, Iwo 1, no. 1 (2024): 100–110. https://doi.org/10.5281/zenodo.15106113.

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This study presents a new modified Adomian decomposition approach for solving Volterra-Fredholm integro-differential equations. The suggested approach attempts to improve the efficiency and accuracy of the present method for dealing with this class of equations. The modified Adomian decomposition approach was shown to be useful in generating trustworthy solutions for a wide variety of Volterra-Fredholm integro-differential equations. Our discoveries help to enhance numerical methods for solving integro-differential equations, which have applications in a variety of scientific and engineering a

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Amal M. Wadi. "Using W Transform for Solving Volterra Integro-Differential Equations." Communications on Applied Nonlinear Analysis 32, no. 7s (2025): 675–87. https://doi.org/10.52783/cana.v32.3474.

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There are numerous uses for the Volterra integro-differential equation in the fields of mechanics, geometric probability, population dynamics, theory of rejuvenation, facts on particle size and the damping of string vibration, and transmission of heat issues. Finding the approximate or exact solutions to these equations is of interest to many mathematicians and scientists. Our aim of this paper is to explore and figure out the solution of the Volterra integro-differential equation with a convolution kernel. We now introduce the W transform for determining the solution of linear Volterra integr

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Tunç, Cemil, Fehaid Salem Alshammari та Fahir Talay Akyıldız. "On the Existence of Solutions and Ulam-Type Stability for a Nonlinear ψ-Hilfer Fractional-Order Delay Integro-Differential Equation". Fractal and Fractional 9, № 7 (2025): 409. https://doi.org/10.3390/fractalfract9070409.

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In this work, we address a nonlinear ψ-Hilfer fractional-order Volterra integro-differential equation that incorporates n-multiple-variable time delays. Employing the ψ-Hilfer fractional derivative operator, we investigate the existence of a unique solution, as well as the Ulam–Hyers–Rassias stability, semi-Ulam–Hyers–Rassias stability, and Ulam–Hyers stability of the proposed ψ-Hilfer fractional-order Volterra integro-differential equation through the fixed-point approach. In this study, we enhance and generalize existing results in the literature on ψ-Hilfer fractional-order Volterra integro

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Dissertations / Theses on the topic "Volterra integro-differential equations"

1

Roberts, Jason Anthony. "Numerical analysis of Volterra integro-differential equations." Thesis, University of Liverpool, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.367635.

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Parsons, Wade William. "Waveform relaxation methods for Volterra integro-differential equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0013/NQ52694.pdf.

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Iragi, Bakulikira. "On the numerical integration of singularly perturbed Volterra integro-differential equations." University of the Western Cape, 2017. http://hdl.handle.net/11394/5669.

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Magister Scientiae - MSc<br>Efficient numerical approaches for parameter dependent problems have been an inter- esting subject to numerical analysts and engineers over the past decades. This is due to the prominent role that these problems play in modeling many real life situations in applied sciences. Often, the choice and the e ciency of the approaches depend on the nature of the problem to solve. In this work, we consider the general linear first-order singularly perturbed Volterra integro-differential equations (SPVIDEs). These singularly perturbed problems (SPPs) are governed by int

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Tarang, Mare. "Stability of the spline collocation method for Volterra integro-differential equations." Online version, 2004. http://dspace.utlib.ee/dspace/bitstream/10062/793/5/Tarang.pdf.

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Nguyen, Hoan Kim Huynh. "Volterra Systems with Realizable Kernels." Diss., Virginia Tech, 2004. http://hdl.handle.net/10919/11153.

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We compare an internal state method and a direct Runge-Kutta method for solving Volterra integro-differential equations and Volterra delay differential equations. The internal state method requires the kernel of the Volterra integral to be realizable as an impulse response function. We discover that when applicable, the internal state method is orders of magnitude more efficient than the direct numerical method. However, constructing state representation for realizable kernels can be challenging at times; therefore, we propose a rational approximation approach to avoid the problem. Th

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Wilkinson, Joan Christina. "Stability in the numerical treatment of Volterra integral and integro-differential equations with emphasis on finite recurrence relations." Thesis, Open University, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.290222.

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Ahlip, Rehez Ajmal. "Stability & filtering of stochastic systems." Thesis, Queensland University of Technology, 1997.

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Shakourifar, Mohammad. "Reliable Approximate Solution of Systems of Delay Volterra Integro-differential Equations." Thesis, 2013. http://hdl.handle.net/1807/35992.

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Ordinary and partial differential equations are often derived as a first approximation to model a real-world situation, where the state of the system depends not only on the present time, but also on the history of the system. In this situation, a higher level of realism can be achieved by incorporating distributed delays in the mathematical models described by differential equations which results in delay Volterra integro-differential equations (denoted DVIDEs). Although DVIDEs serve as indispensable tools for modelling real systems, we still lack efficient and reliable software to approxima

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Huang, Yu-Shiang, and 黃毓翔. "SOLUTIONS OF SYSTEMS OF LINEAR FREDHOLM-VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS BY USING CHEBYSHEV POLYNOMIALS." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/63301101432057539009.

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碩士<br>大同大學<br>應用數學學系(所)<br>94<br>A matrix method called the Chebyshev collocation method is used to solve a systems of higher-order linear integro-differential equations numerically. We use truncated Chebyshev series and Chebyshev collocation points to transform the systems of integro-differential equations and the given conditions into the matrix equations . The method can be proposed to obtain approximate solution and analytical solution of IDEs .Since size of the matrices created by the method are large ,this allow us to use mathematical software .

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Books on the topic "Volterra integro-differential equations"

1

Tang, Arsalang. Analysis and numerics of delay Volterra integro-differential equations. University of Manchester, 1995.

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Vsesoi͡uznyĭ nauchno-issledovatelʹskiĭ institut sistemnykh issledovaniĭ, ред. Integralʹnye i integro-different͡sialʹnye uravnenii͡a Volʹterra s osobymi tochkami: Analiticheskai͡a teorii͡a. VNIISI, 1987.

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3

Jumarhon, B. High order product integration methods for a nonlinear Volterra integro-differential equation. University of Salford Department of Mathematics and Computer Science, 1995.

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Kostic, Marko. Abstract Volterra Integro-Differential Equations. Taylor & Francis Group, 2015.

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Kostic, Marko. Abstract Volterra Integro-Differential Equations. Taylor & Francis Group, 2015.

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Kostic, Marko. Abstract Volterra Integro-Differential Equations. Taylor & Francis Group, 2019.

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Abstract Volterra Integro-Differential Equations. Taylor & Francis Group, 2015.

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8

Saeed, Rostam K., and Omer M. Al-Faour. Computational Methods for Solving System of Volterra Integral Equation: Computational Methods for Solving System of linear Volterra Integral and Integro-differential Equations. LAP Lambert Academic Publishing, 2011.

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Book chapters on the topic "Volterra integro-differential equations"

1

Wazwaz, Abdul-Majid. "Volterra Integro-Differential Equations." In Linear and Nonlinear Integral Equations. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21449-3_5.

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Wazwaz, Abdul-Majid. "Nonlinear Volterra Integro-Differential Equations." In Linear and Nonlinear Integral Equations. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21449-3_14.

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Wazwaz, Abdul-Majid. "Volterra-Fredholm Integro-Differential Equations." In Linear and Nonlinear Integral Equations. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21449-3_9.

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4

Georgiev, Svetlin G. "Generalized Volterra Integro-Differential Equations." In Integral Equations on Time Scales. Atlantis Press, 2016. http://dx.doi.org/10.2991/978-94-6239-228-1_4.

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Rihan, Fathalla A. "Numerical Solutions of Volterra Delay Integro-Differential Equations." In Delay Differential Equations and Applications to Biology. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-0626-7_4.

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Parts, Inga, and Arvet Pedas. "Spline Approximations for Weakly Singular Volterra Integro-Differential Equations." In Integral Methods in Science and Engineering. Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-0-8176-8184-5_29.

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Anakira, N. R., G. F. Bani-Hani, and O. Ababneh. "An Effective Procedure for Solving Volterra Integro-Differential Equations." In Mathematics and Computation. Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-0447-1_40.

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Pandey, Ram K., and Harendra Singh. "An Efficient Numerical Algorithm to Solve Volterra Integral Equation of Second Kind." In Topics in Integral and Integro-Differential Equations. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-65509-9_8.

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Heber, Gerd, and Christoph Lindemann. "Parallel Numerical Solution of a Class of Volterra Integro—Differential Equations." In Stochastic Differential and Difference Equations. Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-1980-4_10.

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Rautian, N. A. "Well-Posedness of Volterra Integro-Differential Equations with Fractional Exponential Kernels." In Differential and Difference Equations with Applications. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-56323-3_39.

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Conference papers on the topic "Volterra integro-differential equations"

1

Oyedepo, Taiye, Matthew O. Oluwayemi, Sunday Emmanuel Fadugba, and Rajiniganth Pandurangan. "A Comparative Study Of Two Computational Techniques for Volterra-Fredholm Integro-Differential Equations." In 2024 International Conference on Science, Engineering and Business for Driving Sustainable Development Goals (SEB4SDG). IEEE, 2024. http://dx.doi.org/10.1109/seb4sdg60871.2024.10629727.

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"Spectral analysis of Volterra integro-differential equations." In Уфимская осенняя математическая школа - 2022. Т.1. Baskir State University, 2022. http://dx.doi.org/10.33184/mnkuomsh1t-2022-09-28.9.

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Vlasov, Victor. "Spectral analysis of Volterra integro-differential equations." In International scientific conference "Ufa autumn mathematical school - 2021". Baskir State University, 2021. http://dx.doi.org/10.33184/mnkuomsh1t-2021-10-06.8.

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Tunç, Cemil. "On qualitative properties in Volterra integro-differential equations." In ICNPAA 2016 WORLD CONGRESS: 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences. Author(s), 2017. http://dx.doi.org/10.1063/1.4972756.

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Mehdiyeva, Galina, Vagif Ibrahimov, and Mehriban Imanova. "One relationship between Volterra integro-differential and ordinary differential equations." In CENTRAL EUROPEAN SYMPOSIUM ON THERMOPHYSICS 2019 (CEST). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5114554.

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Shaw, Ruth E. "A parallel algorithm for nonlinear Volterra integro-differential equations." In the 2000 ACM symposium. ACM Press, 2000. http://dx.doi.org/10.1145/335603.335704.

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Azhmyakov, Vadim, Magnus Egerstedt, and Erik I. Verriest. "On the Optimal Control of Volterra Integro-Differential Equations." In 2019 IEEE 58th Conference on Decision and Control (CDC). IEEE, 2019. http://dx.doi.org/10.1109/cdc40024.2019.9028859.

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Agilan, K., and V. Parthiban. "Existence results for fuzzy fractional Volterra integro differential equations." In 2ND INTERNATIONAL CONFERENCE ON MATHEMATICAL TECHNIQUES AND APPLICATIONS: ICMTA2021. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0108987.

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Pandey, Ram K., and Pooran Lal Prajapati. "Chebyshev spectral collocation method for volterra integro-differential equations." In PROBLEMS IN THE TEXTILE AND LIGHT INDUSTRY IN THE CONTEXT OF INTEGRATION OF SCIENCE AND INDUSTRY AND WAYS TO SOLVE THEM: PTLICISIWS-2. AIP Publishing, 2024. http://dx.doi.org/10.1063/5.0202180.

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Talab ABDULLAH, Jalil, Hayder M AL-SAEDI, and Ali Hussein SHUAA. "SOLVING NON-LINEAR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS USING TOUCHARD METHOD." In VI.International Scientific Congress of Pure,Applied and Technological Sciences. Rimar Academy, 2022. http://dx.doi.org/10.47832/minarcongress6-39.

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In this paper, work effectively built on Touchard polynomials (TPs) was presented to find the solutions of Non-Linear Volterra integro-differential (NLVID) equations of the first, second type and first order. By comparing the exact and approximate solutions for three examples, the accuracy and ability of the offered method were tested. The accuracy of our procedure has been demonstrated by the presented results in tables and graphs. In addition, the solution’s accuracy of this technique has been also presented. All computations and graphics were performed using the MATLAB R2018b programme.

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