Semi-analytical method for blood flow model with source terms

References

• Seadawy A, Iqbal M, Dianchen L. Applications of propagation of long-wave with dissipation and dispersion in nonlinear media via solitary wave solutions of generalized Kadomtsev–Petviashvili modified equal width dynamical equation. Computers Math Appl. 2019;78:3620–3632.
   Web of Science ®Google Scholar
• Seadawy AR, Iqbal M, Lu D. The nonlinear diffusion reaction dynamical system with quadratic and cubic nonlinearities with analytical investigations. Int J Modern Phys B. 2020;34(9):2050085.
   Web of Science ®Google Scholar
• Seadawy AR, Iqbal M, Lu D. Nonlinear wave solutions of the Kudryashov–Sinelshchikov dynamical equation in mixtures liquid–gas bubbles under the consideration of heat transfer and viscosity. J Taibah University Sci. 2019;13(1):1060–1072.
   Web of Science ®Google Scholar
• Nasreen N, Seadawy AR, Lu D, et al. Construction of modulation instability analysis and optical soliton solutions of pertubed nonlinear Schrödinger dynamical equation with power law nonlinearity in non-kerr medium. Res Phys. 2019;13:102263.
   Google Scholar
• Arshad M, Seadawy AR, Lu D, et al. Dispersive solitary wave solutions of strain wave dynamical model and its stability. Commun Theor Phys. 2019;71:1155–1162.
   Web of Science ®Google Scholar
• Chamekh M, Brik N, Abid M. Mathematical and numerical study of the concentration effect of red cells in blood. J King Saud Univ Sci. 2019;31(4):1463–1470.
   Web of Science ®Google Scholar
• Iqbal M, Seadawy AR, Lu D. Construction of solitary wave solutions to the nonlinear modified Kortewege–de Vries dynamical equation in unmagnetized plasma via mathematical methods. Modern Phys Lett. 2018;33(32):1850183.
   Web of Science ®Google Scholar
• Iqbal M, Seadawy AR, Lu D. Dispersive solitary wave solutions of nonlinear further modified Korteweg–de vries dynamical equation in an unmagnetized dusty plasma. Modern Phys Lett. 2018;33(37):1850217.
   Web of Science ®Google Scholar
• Iqbal M, Seadawy AR, Lu D. Applications of nonlinear longitudinal wave equation in a magneto-electro-elastic circular rod and new solitary wave solutions. Modern Phys Lett B. 2019;33(18):1950210.
   Web of Science ®Google Scholar
• Iqbal M, Seadawy AR, Khalil OH, et al. Propagation of long internal waves in density stratified ocean for the (2 + 1)-dimensional nonlinear Nizhnik–Novikov–Vesselov dynamical equation. Res Phys. 2020;16:102838.
   Google Scholar
• Seadawy AR, Iqbal M, Lu D. Propagation of kink and anti-kink wave solitons for the nonlinear damped modified Korteweg–de Vries equation arising in ion-acoustic wave in an unmagnetized collisional dusty plasma. Physica A. 2020;544:123560.
   Web of Science ®Google Scholar
• Arshad M, Seadawy AR, Lu D, et al. Elliptic function solutions, modulation instability and optical solitons analysis of the paraxial wave dynamical model with kerr media. Opt Quantum Electron. 2021;53:7.
   Web of Science ®Google Scholar
• Arshad M, Lu D, Wang J. (N+1)-dimensional fractional reduced differential transform method for fractional order partial differential equations. Commun Nonlinear Sci Numerical Simul. 2017;48:509–519.
   Web of Science ®Google Scholar
• Barati S, Ivaz K. Variational iteration method for solving systems of linear delay differential equations. Int J Comput Math Sci. 2012;6:132–135.
   Google Scholar
• Alderremy AA, Elzaki TM, Chamekh M. New transform iterative method for solving some Klein–Gordon equations. Res Phys. 2018;10:655–659.
   Google Scholar
• Elzaki MT, Chamekh M. Solving nonlinear fractional differential equations using a new decomposition method. Universal J Appl Math Comput. 2018;6:27–35.
   Google Scholar
• Chamekh M, Elzaki TM. Explicit solution for some generalized fluids in laminar flow with slip boundary conditions. J Math Computer Sci. 2018;18:72–281.
   Web of Science ®Google Scholar
• Chamekh M, Latrach MA, Jday F. Multi-step semi-analytical solutions for a CHIKungunya virus system. J Umm Al-Qura Univ Appl Sci. 2023.
   Google Scholar
• He JH. Variational iteration method – a kind of non-linear analytical technique: some examples. The variational iteration method: a reliable analytic tool for solving linear and nonlinear wave equations. Int J Non-Linear Mech. 1999;34:699–708.
   Web of Science ®Google Scholar
• He JH. Some asymptotic methods for strongly nonlinear equations. Int J Modern Phys B. 2006;20(10):1141–1199.
   Web of Science ®Google Scholar
• Wazwaz AM. The variational iteration method for solving linear and nonlinear systems of PDEs. Computers Math Appl. 2007;54:895–902.
   Web of Science ®Google Scholar
• Wazwaz AM. The variational iteration method: a reliable analytic tool for solving linear and nonlinear wave equations. Computers Math Appl. 2007;54:926–932.
   Web of Science ®Google Scholar
• Bertaglia G, Caleffi V, Valiani A. Modeling blood flow in viscoelastic vessels: the 1D augmented fluid-structure interaction system. Comput Methods Appl Mech Eng. 2020;360:112772.
   Web of Science ®Google Scholar
• Krivovichev GV. Computational analysis of one-dimensional models for simulation of blood flow in vascular networks. J Comput Sci. 2022;62:101705.
   Web of Science ®Google Scholar
• Quarteroni A. Cardiovascular mathematics. In: Proceedings of the International Congress of Mathematicians, Madrid, Spain; 2006.
   Google Scholar
• Quarteroni A, Valli A. Domain decomposition methods for partial differential equations. Oxford: International Oxford University Press; 1999.
   Google Scholar
• Quarteroni A, Tuveri M, Veneziani A. Computational vascular fluid dynamics: problems, models and methods. Comput Vis Sci. 2000;2(4):163–197.
   Google Scholar
• Quarteroni A, Veneziani A. Analysis of a geometrical multiscale model based on the coupling of ODE and PDE for blood flow simulations. Multiscale Modeling Simul. 2003;1:173–195.
   Web of Science ®Google Scholar
• Bessonov N, Sequeira A, Simakov S, et al. Methods of blood flow modelling. Math Model Nat Phenom. 2016;11:1–25.
   Web of Science ®Google Scholar
• Čanić S, Kim EH. Mathematical analysis of the quasilinear effects in a hyperbolic model blood flow through compliant axi-symmetric vessels. Math Methods Appl Sci. 2003;26:1161–1186.
   Web of Science ®Google Scholar
• Formaggia L, Veneziani A. Reduced and multiscale models for the human cardiovascular system. Lecture notes VKI lecture series, researchgate.net 2003.
   Google Scholar
• Brook BS, Falle SAEG, Pedley TJ. Numerical solutions for unsteady gravity-driven flows in collapsible tubes: evolution and roll-wave instability of a steady state. J Fluid Mech. 1999;396:223–256.
   Web of Science ®Google Scholar
• Kholodov AS. Some dynamical models of external breathing and haemodynamics accounting for their coupling and substance transport. Computer models and medicine progress. Moscow: Nauka; 2001. p. 127–163 (Russian).
   Google Scholar
• Müller LO, Parés C, Toro E. Well-balanced high-order numerical schemes for one-dimensional blood flow in vessels with varying mechanical properties. J Comput Phys. 2013;242:53–85.
   Web of Science ®Google Scholar