Research Papers On Ordinary Differential Equations

  • 1.

    Rui-xia, L., Zhi-qing, H.: Numerical methods of differential equations. East China University of Technology Press (2005)Google Scholar

  • 2.

    Ji-ming, Y.: A formula to solve initial value problem of homogeneous linear differential equations with constant coefficients and its application. Yantai Teachers University Journal 16(1), 8–13 (2000)Google Scholar

  • 3.

    Yan, W., Ji-en, D.: Discuss the solution of First Order Linear Differential Equations. China Education Innovation Herald. No. 01 (2010)Google Scholar

  • 4.

    Hong-tian, J.: Non-linear odrdiary differential equation of first order with method of lerding variables. Journal of YanBei Teacher’s College 15(6) (1999)Google Scholar

  • 5.

    Qing-yang, L., Neng-chao, W., Da-yi, Y.: Numerical analysis. Tsinghua University Press, Beijing (2001)Google Scholar

  • 6.

    Kim, D., Stanescu, D.: Low-storang Runge-Kutta methods for stochastic differential equations. Applied Numerical Mathematics 58 (2008)Google Scholar

  • 7.

    Wang, P.: Three-stage stochastic Runge-kutta methods for stochastic differential equations. Journal of Computational and Applied Mathematics 222, 324–332 (2008)MathSciNetCrossRefMATHGoogle Scholar

  • 8.

    Northeast Normal University. Ordinary differential equations. Higher Education PressGoogle Scholar

  • 9.

    Da-xue, Q., Lin-long, Z.: Discussion on the Integrable Conditions of Riccati Equation. Journal of Xi an University of Arts and Science (Natural Science Edition) 9(1) (January 2006)Google Scholar

  • 10.

    Nakamura, S.: Numerical analysis and graphic visualization with MATLAB. Electronics Industry Press (2005)Google Scholar

  • Calculating the value of $C^{k\in\{1,\infty\}}$ class of smoothness real-valued function's derivative in point of $\mathbb{R}^+$ in radius of convergence of its Taylor polynomial (or series), applying an analog of Newton's binomial... more

    Calculating the value of $C^{k\in\{1,\infty\}}$ class of smoothness real-valued function's derivative in point of $\mathbb{R}^+$ in radius of convergence of its Taylor polynomial (or series), applying an analog of Newton's binomial theorem and $q$-difference operator. $(P,q)$-power difference introduced in section 5. Additionally, by means of Newton's interpolation formula, the discrete analog of Taylor series, interpolation using $q$-difference and $p,q$-power difference is shown.

    Keywords: Power function, Monomial, Polynomial, Power series (mathematics), Exponential function, Power (mathematics), Exponentiation, Mathematical Series, Cube (Algebra), Euler number, Perfect cube, Diophantine equations, Finite difference, Derivative, Divided difference, High order finite difference, Ordinary differential equation, Partial differential equation, Partial derivative, Partial difference, High order derivative, Differential calculus, Calculus, Differential equations, Differentiation, Derivatives, Finite differences, Difference Equations, Numerical Differentiation, Finite difference coefficient, Forward Finite Difference, Backward Finite Difference, Central Finite difference, Binomial coefficient, Newton's Binomial Theorem, Pascal’s triangle, Binomial Series, Binomial theorem, Newton's interpolation formula, Binomial expansion, Pascal triangle, Multinomial theorem, Binomial Sum, Mathematics, Math, Maths, Science, Algebra, Number theory, Numerical analysis, Mathematical analysis, Functional analysis, STEM, Numercal methods, Classical Analysis and ODEs, Analysis of PDEs, General Mathematics, Discrete Mathematics, Applied Mathematics, Calculus of variations, q-derivative, Jackson derivative, q-calculus, h-calculus, Quantum calculus, q-difference, Quantum algebra, Qunatum calculus, Hypergeometric series, Hypergeometric function, Time Scale Calculus, Power quantum calculus, Quantum difference, Quantum variatoinal calculus, h-difference, arXiv, Preprint, Open science, arXiv.org, Open access, 0000-0002-6544-8880, Series Expansion, Taylor's theorem, Taylor's formula, Taylor's series, Taylor's polynomial, Analytic function, Series representation, Polynomial expansion, Taylor theorem, Taylor formula, Taylor series, Taylor polynomial, Maclaurin Series, Petro Kolosov, Kolosov Petro, Kolosov, kolosov_p_1, KolosovP, kolosov_petro, petro-kolosov, kolosov-petro, petrokolosov, kolosov.petro, Kolosov_Petro, petro.kolosov.9

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