Abstract
We apply the reproducing kernel Hilbert space method to a class of nonlinear systems of partial differential equations and to get multiple solutions of second order differential equations. We have reached meaningful results. These results have been depicted by figures. This method is a very impressive technique for solving nonlinear systems of partial differential equations and second order differential equations.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Abbasbandy, S., Azarnavid, B., Alhuthali, M.S.: A shooting reproducing kernel Hilbert space method for multiple solutions of nonlinear boundary value problems. J. Comput. Appl. Math. 279, 293–305 (2015)
Akgül, A.: A new method for approximate solutions of fractional order boundary value problems. Neural Parallel Sci. Comput. 22(1–2), 223–237 (2014)
Castro, L.P., Rodrigues, M.M., Saitoh, S.: A fundamental theorem on initial value problems by using the theory of reproducing kernels. Complex Anal. Oper. Theory 9(1), 87–98 (2015)
Cui, M., Lin, Y.: Nonlinear Numerical Analysis in the Reproducing Kernel Space. Nova Science, New York (2009)
Inc, M., Akgül, A., Geng, F.: Reproducing kernel Hilbert space method for solving Bratu’s problem. Bull. Malays. Math. Sci. Soc. 38, 271–287 (2015)
Ketabchi, R., Mokhtari, R., Babolian, E.: Some error estimates for solving Volterra integral equations by using the reproducing kernel method. J. Comput. Appl. Math. 273, 245–250 (2015)
Mohammadi, M., Mokhtari, R.: A reproducing kernel method for solving a class of nonlinear systems of PDEs. Math. Model. Anal. 19(2), 180–198 (2014)
Zayed, A.I.: Solution of the energy concentration problem in reproducing-kernel Hilbert space. SIAM J. Appl. Math. 75(1), 21–37 (2015)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Akgül, A., Akgül, E.K., Khan, Y., Baleanu, D. (2019). Comparison on Solving a Class of Nonlinear Systems of Partial Differential Equations and Multiple Solutions of Second Order Differential Equations. In: Taş, K., Baleanu, D., Machado, J. (eds) Mathematical Methods in Engineering. Nonlinear Systems and Complexity, vol 23. Springer, Cham. https://doi.org/10.1007/978-3-319-91065-9_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-91065-9_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-91064-2
Online ISBN: 978-3-319-91065-9
eBook Packages: EngineeringEngineering (R0)