پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شماره‌ها | 641 |
| تعداد مقالات | 9,358 |
| تعداد مشاهده مقاله | 68,014,485 |
| تعداد دریافت فایل اصل مقاله | 28,167,095 |
About solving stochastic It\^{o}-Volterra integral equations using the spectral collocation method | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 2، دوره 12، شماره 2، بهمن 2021، صفحه 11-24 اصل مقاله (507.09 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2019.13154.1680 | ||
| نویسندگان | ||
| Zeinab Taheri Tari* ؛ Shahnam Javadi؛ Esmail Babolian | ||
| Department of Mathematics, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran | ||
| تاریخ دریافت: 29 آبان 1396، تاریخ بازنگری: 17 اسفند 1396، تاریخ پذیرش: 13 آبان 1398 | ||
| چکیده | ||
| The purpose of this paper is to propose the spectral collocation method to solve linear and nonlinear stochastic It^o-Volterra integral equations (SVIEs). The proposed approach is different from other numerical techniques as we consider the Legendre Gauss type quadrature for estimating It^o integrals. The main characteristic of the presented method is that it reduces SVIEs into a system of algebraic equations. Thus, we can solve the problem by Newton's method. Furthermore, the convergence analysis of the approach is established. The method is computationally attractive, and to reveal the accuracy, validity, and efficiency of the proposed method, some numerical examples and convergence analysis are included. | ||
| کلیدواژه‌ها | ||
| stochastic؛ It^o-Volterra integral equations؛ collocation؛ shifted Legendre polynomials؛ Gauss type quadrature | ||
| مراجع | ||
|
[1] M. Berger and V. Mizel, Volterra equations with Itˆo integrals I, J. Integral Eq. 2 (1980) 187–245. [2] M. Berger and V. Mizel, Volterra equations with Itˆo integrals II, J. Integral Eq. 2 (1980) 319–337. [3] D. Kun, L. Guo and G. Guiding, A class of control variates for pricing Asian options under stochastic Volatility models, IAENG Int. J. Appl. Math. 43(2) (2013) 45–53. [4] D. Kun, L. Guo and G. Guiding, Accelerating Monte Carlo method for pricing multi-asset options under stochastic Volatility Models, IAENG Int. J. Appl. Math. 44(2) (2014) 62–70. [5] M. Khodabin, K. Maleknejad and F. Hosseini Shekarabi, Application of triangular functions to numerical solution of stochastic Volterra integral equations, IAENG Int. J. Appl. Math. 43(1) (2011) 1–9. [6] M. Khodabin, K. Maleknejad, M. Rostami, and M. Nouri, Numerical solution of stochastic differential equations by second order Runge-Kutta methods, Math. Comput. Model. 53 (2011) 1910–1920. [7] F.C. Klebaner, Intoduction to stochastic calculus with applications, Monash University, Australia, Second edition, 2005. [8] P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Appl. Math. Springer-Verlag, Berlin, 1999. [9] K. Maleknejad, M. Khodabin and M. Rostami, Numerical solution of stochastic Volterra integral equations by stochastic operational matrix based on block pulse functions, Math. Comput. Model. 2011 (2011) 791–800. [10] C.I. Nkeki, Continuous time mean-variance portfolio selection problem with stochastic salary and strategic consumption planning for a defined contribution Pension scheme, IAENG Int. J. Appl. Math. 44(2) (2014) 71–82. [11] C.H. Wena and T.S. Zhangc, Improved rectangular method on stochastic Volterra equations, J. Comput. Appl. Math. 235 (2011) 2492–2501. [12] I. Ichiro, On the existence and uniqueness of solutions of stochastic integral equations of the Volterra type, Kodai Math. J. 2(2) (1979) 158–170. [13] Z. Wang, Existence-uniqueness of solutions to stochastic Volterra equations with singular kernels and nonLipschitz coefficients, Stat. Probab. Lett. 78(9) (2008) 1062–1071. [14] X. Zhang, Euler schemes and large deviations for stochastic Volterra equations with singular kernels, J. Diff. Eq. 224 (2008) 2226–2250. [15] E. Celik and K. Tabatabaei, Solving a class of Volterra integral equation systems by the differential transform method, Int. J. Nonlinear Sci. 16(1) (2013) 87–91. [16] J.J. Levin and J.A. Nohel, On a system of integro-differential equations occurring in reactor dynamics, J. Math. Mech. 9 (1960) 347–368. [17] R.K. Miller, On a system of integro-differential equations occurring in reactor dynamics, SIAM J. Appl. Math. 14 (1966) 446–452. [18] M. N. Oguztoreli, Time-Lag Control Systems, Academic Press, New York, 1966. [19] M. Murge and B. Pachpatte, Successive approximations for solutions of second order stochastic integro-differential equations of Itˆo type, Indian J. Pure. Appl. Math. 21(3) (1990) 260–274. [20] S. Jankovic and D. Ilic, One linear analytic approximation for stochastic integro-differential equations, Acta Math. Sci. 30 (2010) 1073–1085. [21] J. C. Cortes, L. Jodar and L. Villafuerte, Numerical solution of random differential equations: a mean square approach, Math. Comput. Model. 45 (2007) 757–765. [22] J. Cortes, L. Jodar and L. Villafuerte, Mean square numerical solution of random differential equations: facts and possibilities, Comput. Math. Appl. 53 (2007) 1098–1106. [23] Y. Saito and T. Mitsui, Simulation of stochastic differential equations, Ann. Inst. Stat. Math. 45(3) (1993) 419–432. [24] M. H. Heydari, et al. A computational method for solving stochastic Itˆo-Volterra integral equations based on stochastic operational matrix for generalized hat basis functions, J. Comput. Phys. 270 (2014) 402–415. [25] F. Mirzaee and E. Hadadiyan, A collocation technique for solving nonlinear Stochastic Itˆo-Volterra integral equations, Appl. Math. Comput. 247 (2014) 1011–1020. [26] F. Mohammadi, Second kind Chebyshev wavelet Galerkin method for stochastic Itˆo-Volterra integral equations, Mediter. J. Math. 13 (2016) 2613–2631. [27] F. Mohammadi, A wavelet-based computational method for solving stochastic Itˆo–Volterra integral equations, J. Comput. Phys. 298 (2015) 254–265. [28] J. Shen, T. Tang and L. Wang, Spectral methods: algorithms, analysis and applications. Vol. 41. Springer Science and Business Media, 2011. [29] B. Oksendal, Stochastic Differential Equations, An Introduction with Applications, Fifth Edition, Springer-Verlag, New York, 1998. | ||
|
آمار تعداد مشاهده مقاله: 16,148 تعداد دریافت فایل اصل مقاله: 4,824 |
||