Numerical method of solution to loaded nonlocal boundary value problems for ordinary differential equations

Ya. D. Tamarkin, On Some General Problems in the Theory of Ordinary Differential Equations and on Series Expansions of Arbitrary Functions (Petrograd, 1917) [in Russian].

A. Kneser, Die Integralgleichungen und ihre Anwendung in der Matem. Phusik (1923).

Ch. J. de la Vallée-Poussin, “Sur l’équation différentielle linéaire du second ordre: Détermination d’une integrale par deux valeurs assignées: Extension aux équations d’ordre n,” J. Math. Pures Appl. 8(9), 125–144 (1929).

L. Lichtenstein, Vorlesungen über einege Klassen nichtlinear Integralgleichungen und Integraldifferentialgleihungen nebst Anwendungen (Springer, Berlin, 1932).

N. M. Gyunter, “General theory of integral equations,” Dokl. Akad. Nauk SSSR 22, 215–219 (1939).

A. D. Iskenderov, “Mixed problem for loaded quasilinear hyperbolic equations,” Dokl. Akad. Nauk SSSR 199, 1237–1239 (1971).

A. M. Nakhushev, “On the Darboux problem for a nondegenerate loaded integrodifferential equation of the second order,” Differ. Uravn. 12(1), 103–108 (1976).

Kh. Zh. Dikinov, A. A. Kerefov, and A. M. Nakhushev, “On a boundary value problem for the loaded heat equation,” Differ. Equations 12(1), 177–179 (1976).

A. V. Borodin, “An estimate for elliptic equations and its applications to loaded equations,” Differ. Uravn. 13(1), 17–23 (1977).

A. M. Nakhushev, Equations of Mathematical Biology (Vysshaya Shkola, Moscow, 1995) [in Russian].

A. M. Nakhushev, Loaded Equations and Applications (Nauka, Moscow, 2012) [in Russian].

M. Kh. Shkhanukov-Lafishev, “Locally one-dimensional scheme for a loaded heat equation with robin boundary conditions,” Comput. Math. Math. Phys. 49, 1167–1174 (2009).

M. T. Dzhenaliev, On the Theory of Linear Boundary Value Problems for Loaded Differential Equations (Almaty, 1995) [in Russian].

A. A. Tokova, “Boundary value problem for loaded differential equation,” Dokl. Adyg. (Cherkes.) Mezhdunar. Akad. Nauk 7(2), 56–61 (2005).

I. T. Kiguradze, “Boundary value problems for system of ordinary differential equations,” Itogi Nauki Tekh. Sovrem. Probl. Mat. Nov. Dostizheniya 30, 3–103 (1987).

M. N. Yakovlev, “Estimates for solutions to systems of loaded integro-differential equations subject to multipoint and integral boundary conditions,” Zap. Nauchn. Sem. LOMI 124, 131–139 (1983).

A. A. Alikhanov, A. M. Berezkov, and M. Kh. Shkhanukov-Lafishev, “Boundary value problems for certain classes of loaded differential equations and solving them by finite difference methods,” Comput. Math. Math. Phys. 48, 1505–1515 (2008).

K. R. Aida-zade, “On the solution of systems of differential equations with nonlocal conditions,” Vychisl. Tekhnol. 1(9), 11–25 (2005).

V. M. Abdullaev and K. R. Aida-zade, “On the numerical solution of loaded systems of ordinary differential equations,” Comput. Math. Math. Phys. 44, 1585–1595 (2004).

K. R. Aida-zade and V. M. Abdullaev, “Numerical solution of systems of differential equations with nonseparated point and integral conditions,” Izv. Vyssh. Tekh. Uchebn. Zaved. Az. Ser. Inf. Avtom. 13(4), 64–70 (2011).

V. M. Abdullaev and K. R. Aida-zade, “On the numerical solution of optimal control problems with nonseparated multipoint and integral conditions,” Vychisl. Mat. Mat. Fiz. 52, 2163–2177 (2012).

V. M. Abdullaev, “Solution of differential equations with nonseparated multipoint and integral conditions,” Sib. Zh. Ind. Mat. 15(3), 3–15 (2012).

S. K. Godunov, “Numerical solution of boundary value problems for systems of linear ordinary differential equations,” Usp. Mat. Nauk 16(3(99)), 171–175 (1961).

A. A. Abramov, “A variation of the ‘dispersion’ method,” USSR Comput. Math. Math. Phys. 1, 368–371 (1961).

E. Rothe, “Zweidimensionale parabolische Randwertaufgaben als Grenzfall Eindimensionaler Randwertaufgaben,” Math. Ann. 102, 650–670 (1930).