CAS wavelets analytic solution and Genocchi polynomials numerical solutions for the integral and integro-differential equations

References

• D. Han, X. Shang, Numerical solution of integro-differential equations by using CAS wavelet operational matrix od integration. Applied Mathematics and Computation. 194, 460-466 (2007). doi: 10.1016/j.amc.2007.04.048
   Web of Science ®Google Scholar
• M. Kot, Elements of Mathematical Ecology, Cambridge University Press, 2001.
   Google Scholar
• D. B. Pougaza. The Lotka integral equation as a stable population model. Postgraduate Essay, African Institute for Mathematical Sciences (AIMS), 2007.
   Google Scholar
• I. D. Kopeikin, V. P. Shishkin, Integral form of the general solution of equations of steady-state thermoelasticity, J. Appl. Math. Mech. (PMM U.S.S.R.). 48 (1) (1984) 117–119. doi: 10.1016/0021-8928(84)90121-7
   Google Scholar
• A. J. Lotka, On an integral equation in population analysis, Ann. Math. Stat 10 (1939) 144–161. doi: 10.1214/aoms/1177732213
   Google Scholar
• S. Yuzbas, M. Sezer, B. Kemanc, Numerical solutions of integro-differential equations and application of a population model with an improved Legendre method, Applied Mathematical Modelling 37 (2013) 2086–2101. doi: 10.1016/j.apm.2012.05.012
   Web of Science ®Google Scholar
• H. Danfu, S. Xufeng, Numerical solution of integro-differential equations by using CAS wavelet operational matrix of integration, Applied Mathematics and Computation 194 (2007) 460–466. doi: 10.1016/j.amc.2007.04.048
   Web of Science ®Google Scholar
• N. Kurta, M. Sezer, Polynomial solution of high-orderlinear Fredholm integro-differential equations with constant coefficients, Journal of the Franklin Institute 345 (2008) 839–850. doi: 10.1016/j.jfranklin.2008.04.016
   Web of Science ®Google Scholar
• M.T. Kajani, M. Ghasemi, E. Babolian, Numerical solution of linear integro-differential equation by using sine–cosine wavelets, Applied Mathematics and Computation 180 (2006) 569–574. doi: 10.1016/j.amc.2005.12.044
   Web of Science ®Google Scholar
• S. Yalcinbas, M. Sezer, H.H. Sorkun, Legendre polynomial solutions of high-order linear Fredholm integro-differential equations, Applied Mathematics and Computation 210 (2009) 334–349. doi: 10.1016/j.amc.2008.12.090
   Web of Science ®Google Scholar
• A. Arikoglu, I. Ozkol, Solutions of integral and integro-differential equation systems by using differential transform method, Computers and Mathematics with Applications 56 (2008) 2411–2417. doi: 10.1016/j.camwa.2008.05.017
   Web of Science ®Google Scholar
• D. Bahuguna, A. Ujlayan, D.N. Pandey, A comparative study of numerical methods for solving an integro-differential equation, Computers and Mathematics with Applications 57 (2009) 1485-1493. doi: 10.1016/j.camwa.2008.10.097
   Web of Science ®Google Scholar
• Y. Wang, L. Zhu, Solving nonlinear Volterra integro-differential equations of fractional order by using Euler wavelet method, Advances in Difference Equations, 2017 (2017) 1-16. doi: 10.1186/s13662-016-1057-2
   Google Scholar
• S. U. Islam, I. Aziz, M. Fayyaz, A new approach for numerical solution of integro-differential equations via Haar wavelets, International Journal of Computer Mathematics, 90(9) (2013) 1971–1989. doi: 10.1080/00207160.2013.770481
   Web of Science ®Google Scholar
• M. Dehghan, A. Saadatmandi, Chebyshev finite difference method for Fredholm integro-differential equation, International Journal of Computer Mathematics Vol. 85, No. 1, January 2008, 123–130. doi: 10.1080/00207160701405436
   Web of Science ®Google Scholar
• S. C. Shiralashetti, S. Kumbinarasaiah, R. A. Mundewadi, Bernoulli Wavelet based Numerical Method for the Solution of Abel’s Integral Equations, International Journal of Engineering, Science and Mathematics, 6(8) (2017) 63-70.
   Google Scholar
• S. C. Shiralashetti, R. A. Mundewadi, Numerical Solution of Nonlinear Fredholm Integro-Differential Equations using Leibnitz-Haar Wavelet Collocation Method, Mechanics, Materials Science and Engineering, 06 (2016) 108-119.
   Google Scholar
• M. Lakestania, M. Jokara, M. Dehghanc, Numerical solution of nth-order integro-differential equations using trigonometric wavelets, Mathematical methods in the applied scinces, 34 (2011) 1317–1329. doi: 10.1002/mma.1439
   Web of Science ®Google Scholar
• M.T. Kajani, A.H. Vencheh, Solving linear Integro-differential equations with Legendre wavelets, International Journal of Computer Mathematics, 81(6) (2004)719–726. doi: 10.1080/00207160310001650044
   Web of Science ®Google Scholar
• A. Isah, C. Phang, New operational matrix of derivative for solving non-linear fractional differential equations via Genocchi polynomials, Journal of King Saud University–Science, (2017).
   Web of Science ®Google Scholar
• G. E. Bergum, A. N. Philippou, A. F. Horadam, Applications of Fibonacci Numbers, Volume 4 Proceedings of ‘The Fourth International Conference on Fibonacci Numbers alld Their Applications’, Wake Forest University, N.C., U.S.A., 1990.
   Google Scholar