دانشگاه تبریز
فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

 آمار

تعداد نشریات45
تعداد شماره‌ها1,371
تعداد مقالات16,852
تعداد مشاهده مقاله54,249,408
تعداد دریافت فایل اصل مقاله16,959,125
Sattari Shajari, Paria, Shidfar, Abdollah, Moghaddam, Behrouz. (1402). Inverse coefficient problem in hyperbolic partial differential equations: An analytical and computational exploration. سامانه مدیریت نشریات علمی, 12(2), 304-313. doi: 10.22034/cmde.2023.56266.2352
Paria Sattari Shajari; Abdollah Shidfar; Behrouz Parsa Moghaddam. "Inverse coefficient problem in hyperbolic partial differential equations: An analytical and computational exploration". سامانه مدیریت نشریات علمی, 12, 2, 1402, 304-313. doi: 10.22034/cmde.2023.56266.2352
Sattari Shajari, Paria, Shidfar, Abdollah, Moghaddam, Behrouz. (1402). 'Inverse coefficient problem in hyperbolic partial differential equations: An analytical and computational exploration', سامانه مدیریت نشریات علمی, 12(2), pp. 304-313. doi: 10.22034/cmde.2023.56266.2352
Sattari Shajari, Paria, Shidfar, Abdollah, Moghaddam, Behrouz. Inverse coefficient problem in hyperbolic partial differential equations: An analytical and computational exploration. سامانه مدیریت نشریات علمی, 1402; 12(2): 304-313. doi: 10.22034/cmde.2023.56266.2352

Inverse coefficient problem in hyperbolic partial differential equations: An analytical and computational exploration

Computational Methods for Differential Equations
مقاله 7، دوره 12، شماره 2، خرداد 2024، صفحه 304-313    اصل مقاله (479.99 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.56266.2352
نویسندگان
Paria Sattari Shajari1؛ Abdollah Shidfar2؛ Behrouz Parsa Moghaddam* 1
1Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran.
2Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran.
چکیده
This investigation centers on the analysis of an inverse hyperbolic partial differential equation, specifically addressing a coefficient inverse problem that emerges under the imposition of an over-determination condition. In order to address this challenging problem, we employ the well-established homotopy analysis technique, which has proven to be an effective and reliable approach in similar contexts. By utilizing this technique, our primary objective is to achieve an efficient and accurate solution to the inverse problem at hand. To substantiate the effectiveness and reliability of the proposed method, we present a numerical example as a practical illustration, demonstrating its applicability in real-world scenarios. 
کلیدواژه‌ها
Hyperbolic partial differential equation؛ Coefficient inverse problem؛ Homotopy analysis method
مراجع
  • [1] G. Adomian, Nonlinear stochastic differential equations, J. Math. Anal. Applic., 55 (1976), 441–452.
  • [2] G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Boston, 1994.
  • [3] M. Chen and J. Q. Liu, A numerical algorithm for solving inverse problems of two-dimensional wave equations, J. Comput. Phys., 50 (1983), 193–208.
  • [4] D. Colton and P. Monk, A comparison of two methods for solving the inverse scattering problem for acoustic waves in an inhomogeneous medium, Journal of Computational and Applied Mathematics, 42 (1992), 5–16.
  • [5] D. Colton, A. Kirsch, and L. Pgivarinta, Far field patterns for acoustic waves in an inhomogeneous medium, SlAM J. Math. Anal., 20 (1989), 1472–1483.
  • [6] D. Colton and P. Monk, The inverse scattering problem for time-harmonic acoustic waves in an inhomogeneous medium, Quart. J. Mech. Appl. Math., 41 (1988), 97–125.
  • [7] D. Colton and P. Monk, The inverse scattering problem for time harmonic acoustic waves in an inhomogeneous medium: numerical experiments, IMA J. Appl. Math., 42 (1989), 77–95.
  • [8] D. Colton and P. Monk, A new method for solving the inverse scattering problem for acoustic waves in an inhomogeneous medium, Inverse Problems, 5 (1989), 1013–1026.
  • [9] D. Colton and P. Monk, A new method for solving the inverse scattering problem for acoustic waves in an inhomogeneous medium II, Inverse Problems, 6 (1990), 935–947.
  • [10] V. Isakov, Inverse Problems for Partial Differential Equations, Springer, Second Edition, 2006.
  • [11] S. I. Kabanikhin, Definitions and examples of inverse and ill-posed problems, Journal of Inverse and Ill-posed Problems, 16 (2008), 317–357.
  • [12] A. V. Karmishin, A. T. Zhukov, and V. G. Kolosov, Methods of Dynamics Calculation and Testing for Thin-walled Structures (in Russian), Mashinostroyenie, Moscow 1990.
  • [13] A. V. K¸edzierawski, The inverse scattering problem for time-harmonic acoustic waves in an inhomogeneous medium with complex refraction index, Journal of Computational and Applied Mathematics, 47 (1993), 83–100.
  • [14] S. Liang and D. J. Jeffrey, Approximate solutions to a parameterized sixth order boundary value problem, Comput. Math. Appl., 59 (2010), 247–253.
  • [15] S. J. Liao, The proposed homotopy analysis technique for the solution of nonlinear problems, Ph.D. Dissertation, Shanghai Jiao Tong University, Shanghai, 1992 (in English).
  • [16] S. J. Liao, Beyond Perturbation: Introduction to the Homotopy Analysis Method, Chapman & Hall/CRC Press, Boca Raton, 2003.
  • [17] S. J. Liao, On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet, J. Fluid Mech., 488 (2003), 189–212.
  • [18] S. J. Liao, On the homotopy analysis method for nonlinear problems, Appl. Math. Comput., 147 (2004), 499–513.
  • [19] S. J. Liao, Notes on the homotopy analysis method: some definitions and theorems, Commun. Nonlinear Sci. Numer. Simul., 14 (2009), 983-997.
  • [20] S. J. Liao, Homotopy Analysis Method in Nonlinear Differential Equations, Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg, 2012.
  • [21] A. M. Lyapunov, General Problem on Stability of Motion (English translation), Taylor & Francis, London, 1992.
  • [22] A. Molabahrami and A. Shidfar, A study on the PDEs with power-law nonlinearity, Nonlinear Anal. RWA, 11 (2010), 1258–1268.
  • [23] P. Mokhtary, B. Parsa Moghaddam, A. M. Lopes, and J. A. Tenreiro Machado, A computational approach for the non-smooth solution of non-linear weakly singular Volterra integral equation with proportional delay, Numerical algorithms, 83 (2020), 987–1006.
  • [24] Z. S. Mostaghim, B. Parsa Moghaddam, and H. Samimi Haghgozar, Computational technique for simulating variable-order fractional Heston model with application in US stock market, Mathematical Sciences, 12 (2018), 277–283.
  • [25] Z. S. Mostaghim, B. Parsa Moghaddam, and H. Samimi Haghgozar, Numerical simulation of fractional-order dynamical systems in noisy environments, Computational and Applied Mathematics, 37 (2018), 6433–6447.
  • [26] Z. Moniri, B. Parsa Moghaddam, and M. Zamani Roudbaraki, An Efficient and Robust Numerical Solver for Impulsive Control of Fractional Chaotic Systems, Journal of Function Spaces, 2023 (2023).
  • [27] A. H. Nayfeh, Perturbation Methods, John Wiley & Sons, New York, 2000.
  • [28] B. Parsa Moghaddam, A. Dabiri, Z. S. Mostaghim, and Z. Moniri, Numerical solution of fractional dynamical systems with impulsive effects, International Journal of Modern Physics C, 34 (2023), 1–15.
  • [29] V. G. Romanov, Inverse problem,s for the wave equation with an impulse source of unknown form, Doklady Akademii Nauk, 416 (2007), 320–324.
  • [30] M. Sajid, M. Awais, S. Nadeem, and T. Hayat, The influence of slip condition on thin film flow of a fourth grade fluid by the homotopy analysis method, Comput. Math. Appl., 56 (2008), 2019–2026.
  • [31] A. Sami Bataineh, M. S. M. Noorani, and I. Hashim, Approximate analytical solutions of systems of PDEs by homotopy analysis method, Comput. Math. Appl., 55 (2008), 2913–2923.
  • [32] Z. Sharifi, B. Parsa Moghaddam, and M. Ilie, Efficient numerical simulation of fractional-order Van der Pol impulsive system, International Journal of Modern Physics C, (2023).
  • [33] A. Shidfar, A. Babaei, A. Molabahrami, and M. Alinejadmofrad, Approximate analytical solutions of the nonlinear reaction diffusion convection problems, Mathematical and Computer Modelling, 53 (2011), 261-268.
  • [34] A. Shidfar, A. Babaei, and A. Molabahrami, Solving the inverse problem of identifying an unknown source term in a parabolic equation, Computers and Mathematics with Applications, 60 (2010), 1209–1213.
  • [35] A. Shidfar, A. Molabahrami, A. Babaei, and A. Yazdanian, A series solution of the nonlinear Volterra and Fredholm integro-differential equations, Commun. Nonlinear Sci. Numer. Simulat., 15 (2010), 205–215.
  • [36] A. Shidfar and A. Molabahrami, A weighted algorithm based on the homotopy analysis method: Application to inverse heat conduction problems, Commun Nonlinear Sci Numer Simulat, 15 (2010), 2908–2915.
  • [37] J. Sylvester and G. Uhlmann, Inverse problems in anisotropic media, Contemporary mathematics, 122 (1991), 105–117.
  • [38] J. A. Tenreiro Machado, A. Babaei, and B. Parsa Moghaddam, Highly accurate scheme for the Cauchy problem of the generalized Burgers-Huxley equation, Acta Polytechnica Hungarica, 13 (2016).
  • [39] D. S. Tsien and Y. M. Chen, A pulse-spectrum technique for remote sensing of stratified media, Radio Science, 3 (1978), 775–783.
  • [40] B. Van der Pol, On oscillation hysteresis in a simple triode generator, Phil. Mag., 43 (1926), 700–719.
  • [41] M. Yamamoto, Stability, reconstruction formula and regularization for an inverse source hyperbolic problem by a control method, Inverse Problems, 11 (1995), 481–496.
  • [42] M. Yamamoto, On ill-posedness and a Tikhonov regularization for a multidimensional inverse hyperbolic problem, J. Math. Kyoto Univ., 36 (1996), 825–856.
  • [43] M. Yamamoto and X. Zhang, Global uniqueness and stability for an inverse wave source problem for less regular data, Journal of Mathematical Analysis and Applications, 263 (2001), 479–500.
  • [44] U. Yu¨cel, Homotopy analysis method for the sine-Gordon equation with initial conditions, Applied Mathematics and Computation, 203 (2008), 387–395.
آمار
تعداد مشاهده مقاله: 224
تعداد دریافت فایل اصل مقاله: 464


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب