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Journal articles on the topic 'Differential equations'

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Published: 4 June 2021
Last updated: 9 June 2025

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1

Tabor, Jacek. "Differential equations in metric spaces." Mathematica Bohemica 127, no. 2 (2002): 353–60. http://dx.doi.org/10.21136/mb.2002.134163.

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2

Andres, Jan, and Pavel Ludvík. "Topological entropy and differential equations." Archivum Mathematicum, no. 1 (2023): 3–10. http://dx.doi.org/10.5817/am2023-1-3.

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3

Widad, R. Khudair. "On Solving Comfortable Fractional Differential Equations." Journal of Progressive Research in Mathematics 12, no. 5 (November 18, 2017): 2073–79. https://doi.org/10.5281/zenodo.3974845.

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This paper adopts the relationship between conformable fractional derivative and the classical derivative. By using this relation, the comfortable fractional differential equation can transform to a classical differential equation such that the solution of these differential equations is the same. Two examples have been considered to illustrate the validity of our main results.
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4

Laksmikantham, V. "Set differential equations versus fuzzy differential equations." Applied Mathematics and Computation 164, no. 2 (May 2005): 277–94. http://dx.doi.org/10.1016/j.amc.2004.06.068.

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5

Khakale, Savita Santu, Kailas Sahadu Ahire, and Dinkar Pitambar Patil. "Soham Transform in Fractional Differential Equations." Indian Journal Of Science And Technology 17, no. 33 (August 24, 2024): 3481–87. http://dx.doi.org/10.17485/ijst/v17i33.1383.

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Objectives: Soham transforms is one of the appropriate tools for solving fractional differential equations that are flexible enough to adapt to different purposes. Methods: Integral transform methods help to simplify fractional differential equations into algebraic equations. Enable the use of classical methods to solve fractional differential equations. Findings: In this paper, the Soham transform can solve linear homogeneous and non-homogeneous Fractional Differential Equations with constant coefficients. Finally, we use this integral transform to obtain the analytical solution of non-homogeneous fractional differential equations. Novelty: The Soham transform method is a suitable and very effective tool for obtaining analytical solutions of fractional differential equations with constant coefficients. Soham Transform is more multipurpose as the Laplace transform is limited to fractional differential equations. Soham Transform is in the development stage. Keywords: Soham Transform, Fractional Differential Equations, Integral transforms, Reimann­ Liouville Fractional Integral, Caputo Fractional Derivative
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6

Saltas, Vassilios, Vassilios Tsiantos, and Dimitrios Varveris. "Solving Differential Equations and Systems of Differential Equations with Inverse Laplace Transform." European Journal of Mathematics and Statistics 4, no. 3 (June 14, 2023): 1–8. http://dx.doi.org/10.24018/ejmath.2023.4.3.192.

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The inverse Laplace transform enables the solution of ordinary linear differential equations as well as systems of ordinary linear differentials with applications in the physical and engineering sciences. The Laplace transform is essentially an integral transform which is introduced with the help of a suitable generalized integral. The ultimate goal of this work is to introduce the reader to some of the basic ideas and applications for solving initially ordinary differential equations and then systems of ordinary linear differential equations.
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7

Parasidis, I. N. "EXTENSION AND DECOMPOSITION METHOD FOR DIFFERENTIAL AND INTEGRO-DIFFERENTIAL EQUATIONS." Eurasian Mathematical Journal 10, no. 3 (2019): 48–67. http://dx.doi.org/10.32523/2077-9879-2019-10-3-48-67.

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8

Chrastinová, Veronika, and Václav Tryhuk. "Parallelisms between differential and difference equations." Mathematica Bohemica 137, no. 2 (2012): 175–85. http://dx.doi.org/10.21136/mb.2012.142863.

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9

Tumajer, František. "Controllable systems of partial differential equations." Applications of Mathematics 31, no. 1 (1986): 41–53. http://dx.doi.org/10.21136/am.1986.104183.

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10

Kurzweil, Jaroslav, and Alena Vencovská. "Linear differential equations with quasiperiodic coefficients." Czechoslovak Mathematical Journal 37, no. 3 (1987): 424–70. http://dx.doi.org/10.21136/cmj.1987.102170.

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11

Sergey, Piskarev, and Siegmund Stefan. "UNSTABLE MANIFOLDS FOR FRACTIONAL DIFFERENTIAL EQUATIONS." Eurasian Journal of Mathematical and Computer Applications 10, no. 3 (September 27, 2022): 58–72. http://dx.doi.org/10.32523/2306-6172-2022-10-3-58-72.

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We prove the existence of unstable manifolds for an abstract semilinear fractional differential equation Dαu(t) = Au(t) + f(u(t)), u(0) = u 0 , on a Banach space. We then develop a general approach to establish a semidiscrete approximation of unstable manifolds. The main assumption of our results are naturally satisfied. In particular, this is true for operators with compact resolvents and can be verified for finite elements as well as finite differences methods.
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12

Džurina, Jozef. "Comparison theorems for functional differential equations." Mathematica Bohemica 119, no. 2 (1994): 203–11. http://dx.doi.org/10.21136/mb.1994.126077.

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13

qızı, Khudaybergenova Gulayim Sultanbay. "Solving Differential Equations Using Complex Variables." American Journal Of Applied Science And Technology 5, no. 4 (April 1, 2025): 87–89. https://doi.org/10.37547/ajast/volume05issue04-19.

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Solving differential equations is essential in many areas of science and engineering. Traditional methods, however, often become complicated when dealing with oscillatory or complex systems. This article explores how the use of complex variables simplifies the process of solving differential equations. By applying techniques such as Euler’s formula, complexification of real problems, and the Residue Theorem, complex variables provide powerful and elegant methods for finding both real and complex solutions. Several illustrative examples are presented to demonstrate the efficiency and effectiveness of these approaches. The article emphasizes the importance of mastering complex-variable methods for a deeper understanding of differential equations and their applications.
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14

Loud, Warren S., A. N. Tikhonov, A. B. Vasil'eva, and A. G. Sveshnikov. "Differential Equations." American Mathematical Monthly 94, no. 3 (March 1987): 308. http://dx.doi.org/10.2307/2323408.

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15

Croft, Tony, D. A. Sanchez, R. C. Allen Jr., and W. T. Kyner. "Differential Equations." Mathematical Gazette 73, no. 465 (October 1989): 249. http://dx.doi.org/10.2307/3618470.

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16

Brindley, Graham, D. Lomen, and J. Mark. "Differential Equations." Mathematical Gazette 73, no. 466 (December 1989): 353. http://dx.doi.org/10.2307/3619335.

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17

Abbott, Steve, and SMP. "Differential Equations." Mathematical Gazette 79, no. 484 (March 1995): 186. http://dx.doi.org/10.2307/3620064.

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18

Berkshire, Frank, A. N. Tikhonov, A. B. Vasil'eva, and A. G. Sveshnikov. "Differential Equations." Mathematical Gazette 70, no. 452 (June 1986): 168. http://dx.doi.org/10.2307/3615804.

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19

Lee, Tzong-Yow. "Differential Equations." Annals of Probability 29, no. 3 (July 2001): 1047–60. http://dx.doi.org/10.1214/aop/1015345595.

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20

Barrett, K. E. "Differential equations." Applied Mathematical Modelling 11, no. 3 (June 1987): 233–34. http://dx.doi.org/10.1016/0307-904x(87)90010-2.

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21

He, Ji-Huan, and Zheng-Biao Li. "Converting fractional differential equations into partial differential equations." Thermal Science 16, no. 2 (2012): 331–34. http://dx.doi.org/10.2298/tsci110503068h.

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A transform is suggested in this paper to convert fractional differential equations with the modified Riemann-Liouville derivative into partial differential equations, and it is concluded that the fractional order in fractional differential equations is equivalent to the fractal dimension.
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22

Knorrenschild, Michael. "Differential/Algebraic Equations As Stiff Ordinary Differential Equations." SIAM Journal on Numerical Analysis 29, no. 6 (December 1992): 1694–715. http://dx.doi.org/10.1137/0729096.

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23

MANOFF, S. "GEODESIC AND AUTOPARALLEL EQUATIONS OVER DIFFERENTIABLE MANIFOLDS." International Journal of Modern Physics A 11, no. 21 (August 20, 1996): 3849–74. http://dx.doi.org/10.1142/s0217751x96001814.

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The notions of ordinary, covariant and Lie differentials are considered as operators over differentiable manifolds with different (not only by sign) contravariant and covariant affine connections and metric. The difference between the interpretations of the ordinary differential as a covariant basic vector field and as a component of a contravariant vector field is discussed. By means of the covariant metric and the ordinary differential the notion of the line element is introduced and the geodesic equation is obtained and compared with the autoparallel equation.
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24

N O, Onuoha. "Transformation of Parabolic Partial Differential Equations into Heat Equation Using Hopf Cole Transform." International Journal of Science and Research (IJSR) 12, no. 6 (June 5, 2023): 1741–43. http://dx.doi.org/10.21275/sr23612082710.

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25

Marjona, Kosimova. "APPLICATION OF DIFFERENTIAL EQUATIONS IN VARIOUS FIELDS OF SCIENCE." American Journal of Applied Science and Technology 4, no. 6 (June 1, 2024): 76–81. http://dx.doi.org/10.37547/ajast/volume04issue06-15.

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The article, "Application of Differential Equations in Various Fields of Science," explores the use of differential equations for modeling economic and natural phenomena. It examines two main models of economic dynamics: the Evans model for the market of a single product, and the Solow model for economic growth.The author emphasizes the importance of proving the existence of solutions to differential equations in order to verify the accuracy of mathematical models. They also discuss the role of electronic computers in developing the theory of differential equations and its connection with other branches of mathematics such as functional analysis, algebra, and probability theory.Furthermore, the article highlights the significance of various solution methods for differential equations, including the Fourier method, Ritz method, Galerkin method, and perturbation theory.Special attention is paid to the theory of partial differential equations, the theory of differential operators, and problems arising in physics, mechanics, and technology. Differential equations are the theoretical foundation of almost all scientific and technological models and a key tool for understanding various processes in science, such as in physics, chemistry, and biology.Examples of processes described by differential equations include normalreproduction, explosive growth, and the logistic curve. Cases of using differential equations to model deterministic, finite-dimensional, and differentiable phenomena, as well as the impact of catch quotas on population dynamics, are discussed.In conclusion, the significance of differential equations for research and their role in stimulating the development of new mathematical areas is emphasized.
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26

Mona, Hunaiber, and Al-Aati Ali. "SOME FUNDAMENTAL PROPERTIES OF HUNAIBER TRANSFORM AND ITS APPLICATIONS TO PARTIAL DIFFERENTIAL EQUATIONS." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 10, no. 07 (July 20, 2022): 2808–11. https://doi.org/10.5281/zenodo.6866430.

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In this paper, we study some basic properties of a new integral transform '' Hunaiber transform''. Moreover, we apply Hunaiber transform to solve linear partial differential equations with initial and boundary conditions. We solve first order partial differential equations and Second order partial differential equations which are essential equations in mathematical physics and applied mathematics.
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27

Lazopoulos, Konstantinos A. "On Λ-Fractional Differential Equations". Foundations 2, № 3 (5 вересня 2022): 726–45. http://dx.doi.org/10.3390/foundations2030050.

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Λ-fractional differential equations are discussed since they exhibit non-locality and accuracy. Fractional derivatives form fractional differential equations, considered as describing better various physical phenomena. Nevertheless, fractional derivatives fail to satisfy the prerequisites of differential topology for generating differentials. Hence, all the sources of generating fractional differential equations, such as fractional differential geometry, the fractional calculus of variations, and the fractional field theory, are not mathematically accurate. Nevertheless, the Λ-fractional derivative conforms to all prerequisites demanded by differential topology. Hence, the various mathematical forms, including those derivatives, do not lack the mathematical accuracy or defects of the well-known fractional derivatives. A summary of the Λ-fractional analysis is presented with its influence on the sources of differential equations, such as fractional differential geometry, field theorems, and calculus of variations. Λ-fractional ordinary and partial differential equations will be discussed.
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28

L Suresh, P., and Ch Satyanarayana. "Numerical Study of Higher Order Differential Equations Using Differential Transform Method." International Journal of Science and Research (IJSR) 11, no. 9 (September 5, 2022): 1105–7. http://dx.doi.org/10.21275/sr22915122737.

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29

Elishakoff, Isaac. "Differential Equations of Love and Love of Differential Equations." Journal of Humanistic Mathematics 9, no. 2 (July 2019): 226–46. http://dx.doi.org/10.5642/jhummath.201902.15.

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30

Barles, Guy, Rainer Buckdahn, and Etienne Pardoux. "Backward stochastic differential equations and integral-partial differential equations." Stochastics and Stochastic Reports 60, no. 1-2 (February 1997): 57–83. http://dx.doi.org/10.1080/17442509708834099.

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31

Frittelli, Simonetta, Carlos Kozameh, and Ezra T. Newman. "Differential Geometry from Differential Equations." Communications in Mathematical Physics 223, no. 2 (October 1, 2001): 383–408. http://dx.doi.org/10.1007/s002200100548.

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32

Hino, Yoshiyuki, and Taro Yoshizawa. "Total stability property in limiting equations for a functional-differential equation with infinite delay." Časopis pro pěstování matematiky 111, no. 1 (1986): 62–69. http://dx.doi.org/10.21136/cpm.1986.118265.

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33

Chrastina, Jan. "On formal theory of differential equations. I." Časopis pro pěstování matematiky 111, no. 4 (1986): 353–83. http://dx.doi.org/10.21136/cpm.1986.118285.

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34

Chrastina, Jan. "On formal theory of differential equations. II." Časopis pro pěstování matematiky 114, no. 1 (1989): 60–105. http://dx.doi.org/10.21136/cpm.1989.118369.

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35

Li, Tongxing, Yuriy V. Rogovchenko, and Chenghui Zhang. "Oscillation of fourth-order quasilinear differential equations." Mathematica Bohemica 140, no. 4 (2015): 405–18. http://dx.doi.org/10.21136/mb.2015.144459.

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36

Kwapisz, Marian. "On solving systems of differential algebraic equations." Applications of Mathematics 37, no. 4 (1992): 257–64. http://dx.doi.org/10.21136/am.1992.104508.

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37

Franců, Jan. "Weakly continuous operators. Applications to differential equations." Applications of Mathematics 39, no. 1 (1994): 45–56. http://dx.doi.org/10.21136/am.1994.134242.

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38

Grace, S. R., and Bikkar S. Lalli. "Oscillation theorems for certain neutral differential equations." Czechoslovak Mathematical Journal 38, no. 4 (1988): 745–53. http://dx.doi.org/10.21136/cmj.1988.102270.

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39

Ohriska, Ján. "Oscillation of differential equations and $v$-derivatives." Czechoslovak Mathematical Journal 39, no. 1 (1989): 24–44. http://dx.doi.org/10.21136/cmj.1989.102276.

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40

Gopalsamy, K., B. S. Lalli, and B. G. Zhang. "Oscillation of odd order neutral differential equations." Czechoslovak Mathematical Journal 42, no. 2 (1992): 313–23. http://dx.doi.org/10.21136/cmj.1992.128330.

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41

Džurina, Jozef. "Comparison theorem for third-order differential equations." Czechoslovak Mathematical Journal 44, no. 2 (1994): 357–66. http://dx.doi.org/10.21136/cmj.1994.128464.

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42

Grace, S. R., and B. S. Lalli. "Oscillation criteria for forced neutral differential equations." Czechoslovak Mathematical Journal 44, no. 4 (1994): 713–24. http://dx.doi.org/10.21136/cmj.1994.128489.

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43

Fraňková, Dana. "Substitution method for generalized linear differential equations." Mathematica Bohemica 116, no. 4 (1991): 337–59. http://dx.doi.org/10.21136/mb.1991.126028.

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44

Chrastina, Jan. "On formal theory of differential equations. III." Mathematica Bohemica 116, no. 1 (1991): 60–90. http://dx.doi.org/10.21136/mb.1991.126196.

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45

Tiwari, Chinta Mani, and Richa Yadav. "Distributional Solutions to Nonlinear Partial Differential Equations." International Journal of Research Publication and Reviews 5, no. 4 (April 11, 2024): 6441–47. http://dx.doi.org/10.55248/gengpi.5.0424.1085.

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46

Fakorede, E. O. "Evaluation of Differential Equations with Applications to Engineering Problems." Journal of Water Resource Research and Development 4, no. 2 (July 31, 2021): 1–13. https://doi.org/10.5281/zenodo.5150095.

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Several methods for solving ordinary differential equations (ODE) and partial differential equations (PDE) have been developed over the last century. Though the majority of the methods are only useful for academic purposes, some are critical in the solution of real-world problems arising from science and engineering. Only a subset of the available methods for solving (ODE) and (PDE) are discussed in this paper, as it is impossible to cover all of them in a book. Readers are then encouraged to conduct additional research on this topic if necessary. Afterward, the readers are made known to two major numerical methods commonly used by the engineers for the solution of real-life engineering problems.
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47

Song, Liang, Shaodong Chen, and Guoxin Wang. "Oscillation Analysis Algorithm for Nonlinear Second-Order Neutral Differential Equations." Mathematics 11, no. 16 (August 11, 2023): 3478. http://dx.doi.org/10.3390/math11163478.

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Differential equations are useful mathematical tools for solving complex problems. Differential equations include ordinary and partial differential equations. Nonlinear equations can express the nonlinear relationship between dependent and independent variables. The nonlinear second-order neutral differential equations studied in this paper are a class of quadratic differentiable equations that include delay terms. According to the t-value interval in the differential equation function, a basis is needed for selecting the initial values of the differential equations. The initial value of the differential equation is calculated with the initial value calculation formula, and the existence of the solution of the nonlinear second-order neutral differential equation is determined using the condensation mapping fixed-point theorem. Thus, the oscillation analysis of nonlinear differential equations is realized. The experimental results indicate that the nonlinear neutral differential equation can analyze the oscillation behavior of the circuit in the Colpitts oscillator by constructing a solution equation for the oscillation frequency and optimizing the circuit design. It provides a more accurate control for practical applications.
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48

Harir, Atimad, Said Melliani, and Lalla Saadia Chadli. "Fuzzy Conformable Fractional Differential Equations." International Journal of Differential Equations 2021 (February 4, 2021): 1–6. http://dx.doi.org/10.1155/2021/6655450.

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In this study, fuzzy conformable fractional differential equations are investigated. We study conformable fractional differentiability, and we define fractional integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy fractional differential equation by using the concept of conformable differentiability. This concept is based on the enlargement of the class of differentiable fuzzy mappings; for this, we consider the lateral Hukuhara derivatives of order q ∈ 0,1 .
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49

Balamuralitharan, S., and . "MATLAB Programming of Nonlinear Equations of Ordinary Differential Equations and Partial Differential Equations." International Journal of Engineering & Technology 7, no. 4.10 (October 2, 2018): 773. http://dx.doi.org/10.14419/ijet.v7i4.10.26114.

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My idea of this paper is to discuss the MATLAB program for various mathematical modeling in ordinary differential equations (ODEs) and partial differential equations (PDEs). Idea of this paper is very useful to research scholars, faculty members and all other fields like engineering and biology. Also we get easily to find the numerical solutions from this program.
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50

Mwinken, Delphin. "The Interconnection Between Calculus of Variations, Partial Differential Equations and Differential Geometry." Selecciones Matemáticas 11, no. 02 (November 30, 2024): 393–408. https://doi.org/10.17268/sel.mat.2024.02.11.

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Calculus of variations is a fundamental mathematical discipline focused on optimizing functionals, which map sets of functions to real numbers. This field is essential for numerous applications, including the formulation and solution of partial differential equations (PDEs) and the study of differential geometry. In PDEs, calculus of variations provides methods to find functions that minimize energy functionals, leading to solutions of various physical problems. In differential geometry, it helps understand the properties of curves and surfaces, such as geodesics, by minimizing arc-length functionals. This paper explores the intrinsic connections between these areas, highlighting key principles such as the Euler-Lagrange equation, Ekeland’s variational principle, and the Mountain Pass theorem, and their applications in solving PDEs and understanding geometrical structures.
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