Skip to main content
SpringerLink
Log in

A Reproducing Kernel Method for Solving Systems of Integro-differential Equations with Nonlocal Boundary Conditions

  • Research Paper
  • Published:
Iranian Journal of Science and Technology, Transactions A: Science Aims and scope Submit manuscript

Abstract

The aim of this paper is to present a reproducing kernel method for solving system of integro-differential equations with nonlocal boundary conditions. The solution obtained by using the present method takes the form of a convergent series with easily computable components. The analysis of convergence shows that the approximate solution and its derivatives converge to the exact solution and its derivatives, respectively. The numerical examples are given to demonstrate the accuracy of the present method. Results obtained by using the present method are compared with those of the exact solution of each example and are found to be in good agreement.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  • Aronszajn N (1950) Theory of reproducing kernels. Trans Am Math Soc 68:337–404

    Article  MathSciNet  Google Scholar 

  • Babolian E, Javadi S, Moradi E (2016a) RKM for solving Bratu-type differential equations of fractional order. Math Methods Appl Sci 39(6):1548–1557

    Article  MathSciNet  Google Scholar 

  • Babolian E, Javadi S, Moradi E (2016b) Error analysis of reproducing kernel Hilbert space method for solving functional integral equations. J Comput Appl Math 300:300–311

    Article  MathSciNet  Google Scholar 

  • Cui M, Geng F (2007) A computational method for solving one-dimensional variable-coefficient Burgers equation. Appl Math Comput 188:1389–1401

    MathSciNet  MATH  Google Scholar 

  • Cui M, Lin Y (2007) A new method of solving the coefficient inverse problem of differential equation. Sci China A50(4):561–572

    Article  Google Scholar 

  • Cui M, Lin Y (2009) Nonlinear numerical analysis in reproducing kernel Hilbert space. Nova Science Publisher, New York

    MATH  Google Scholar 

  • Fardi M, Ghasemi M, Khoshsiar R (2016) Ghaziani: the reproducing kernel method for some variational problems depending on indefinite integrals. Math Model Anal. https://doi.org/10.3846/13926292.2016.1178185

    Article  MATH  Google Scholar 

  • Geng F, Cui M (2007a) Solving singular nonlinear second-order periodic boundary value problems in the reproducing kernel space. Appl Math Comput 192:389–398

    MathSciNet  MATH  Google Scholar 

  • Geng F, Cui M (2007b) Solving a nonlinear system of second order boundary value problems. J Math Anal Appl 327:1167–1181

    Article  MathSciNet  Google Scholar 

  • Geng F, Cui M (2009) New method based on the HPM and RKHSM for solving forced Duffing equations with integral boundary conditions. J Comput Appl Math 233:165–172

    Article  MathSciNet  Google Scholar 

  • Ghasemi M, Fardi M (2016) Solving Nonlocal initial-boundary value problems for parabolic and hyperbolic integro-differential equations in reproducing kernel Hilbert space. Numer Methods Partial Differ Equ 33:174–198

    MathSciNet  MATH  Google Scholar 

  • Ghasemi M, Fardi M, Khoshsiar R (2015) Ghaziani: numerical solution of nonlinear delay differential equations of fractional order in reproducing kernel Hilbert space. Appl Math Comput 268:815–831

    MathSciNet  MATH  Google Scholar 

  • Vahdati S, Fardi M, Ghasemi M (2017) Option pricing using a computational method based on reproducing kernel. J Comput Appl Math 328:252–266

    Article  MathSciNet  Google Scholar 

  • Yang LH, Shen JH, Wang Y (2012) The reproducing kernel method for solving the system of the linear Volterra integral equations with variable coefficients. J Comput Appl Math 236:2398–2405

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematical Science, Shahrekord University, P. O. Box 115, Shahrekord, Iran

    M. Ghasemi & M. Fardi

  2. Department of Mathematics, Faculty of Mathematical Sciences and Computer, Kharazmi University, 50 Taleghani Avenue, Tehran, 1561836314, Iran

    E. Moradi

Authors
  1. M. Ghasemi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Fardi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. E. Moradi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Ghasemi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ghasemi, M., Fardi, M. & Moradi, E. A Reproducing Kernel Method for Solving Systems of Integro-differential Equations with Nonlocal Boundary Conditions. Iran J Sci Technol Trans Sci 45, 1375–1382 (2021). https://doi.org/10.1007/s40995-021-01089-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40995-021-01089-1

Keywords

AMS Subject Classification

Search

Navigation