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Relevant bibliographies by topics / Differential equations - Numerical methods

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Academic literature on the topic 'Differential equations - Numerical methods'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Differential equations - Numerical methods"

1

Jankowski, Tadeusz, and Marian Kwapisz. "Convergence of numerical methods for systems of neutral functional-differential-algebraic equations." Applications of Mathematics 40, no. 6 (1995): 457–72. http://dx.doi.org/10.21136/am.1995.134307.

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Leversha, Gerry, G. Evans, J. Blackledge, and P. Yardley. "Numerical Methods for Partial Differential Equations." Mathematical Gazette 84, no. 501 (November 2000): 567. http://dx.doi.org/10.2307/3620819.

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T., V., and William F. Ames. "Numerical Methods for Partial Differential Equations." Mathematics of Computation 62, no. 205 (January 1994): 437. http://dx.doi.org/10.2307/2153426.

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Morton, K. W. "NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS." Bulletin of the London Mathematical Society 26, no. 5 (September 1994): 507–8. http://dx.doi.org/10.1112/blms/26.5.507.

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März, Roswitha. "Numerical methods for differential algebraic equations." Acta Numerica 1 (January 1992): 141–98. http://dx.doi.org/10.1017/s0962492900002269.

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Kloeden, Peter, and Eckhard Platen. "Numerical methods for stochastic differential equations." Stochastic Hydrology and Hydraulics 5, no. 2 (June 1991): 172. http://dx.doi.org/10.1007/bf01543058.

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Herdiana, Ratna. "NUMERICAL SIMULATION OF STOCHASTIC DIFFERENTIAL EQUATIONS USING IMPLICIT MILSTEIN METHOD." Journal of Fundamental Mathematics and Applications (JFMA) 3, no. 1 (June 10, 2020): 72–83. http://dx.doi.org/10.14710/jfma.v3i1.7416.

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Stiff stochastic differential equations arise in many applications including in the area of biology. In this paper, we present numerical solution of stochastic differential equations representing the Malthus population model and SIS epidemic model, using the improved implicit Milstein method of order one proposed in [6]. The open source programming language SCILAB is used to perform the numerical simulations. Results show that the method is more accurate and stable compared to the implicit Euler method.

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Ababneh, Osama Y. "New Numerical Methods for Solving Differential Equations." JOURNAL OF ADVANCES IN MATHEMATICS 16 (January 31, 2019): 8384–90. http://dx.doi.org/10.24297/jam.v16i0.8280.

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In this paper, we present new numerical methods to solve ordinary differential equations in both linear and nonlinear cases. we apply Daftardar-Gejji technique on theta-method to derive anew family of numerical method. It is shown that the method may be formulated in an equivalent way as a RungeKutta method. The stability of the methods is analyzed.

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Murphy, R. V. W. "Differential equations - practical methods of numerical solution." Mathematical Gazette 91, no. 521 (July 2007): 227–34. http://dx.doi.org/10.1017/s0025557200181562.

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The most basic problem with differential equations is that of being given an equation that can be put into the formand one pair of solution values x = x0, y = y0, from which to find either an algebraic form of its solution or the numerical value of y corresponding to a particular value of x. This can most conveniently be interpreted as finding, out of the infinity of solution curves to (1.1), an equation for the unique curve that passes through the point (x0, y0) or calculating the coordinates of one particular point on that curve.

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Kim, A. V., and V. G. Pimenov. "Multistep numerical methods for functional differential equations." Mathematics and Computers in Simulation 45, no. 3-4 (February 1998): 377–84. http://dx.doi.org/10.1016/s0378-4754(97)00117-1.

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Dissertations / Theses on the topic "Differential equations - Numerical methods"

1

Keras, Sigitas. "Numerical methods for parabolic partial differential equations." Thesis, University of Cambridge, 1997. https://www.repository.cam.ac.uk/handle/1810/251611.

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Kwok, Ting On. "Adaptive meshless methods for solving partial differential equations." HKBU Institutional Repository, 2009. http://repository.hkbu.edu.hk/etd_ra/1076.

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Saravi, Masoud. "Numerical solution of linear ordinary differential equations and differential-algebraic equations by spectral methods." Thesis, Open University, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.446280.

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This thesis involves the implementation of spectral methods, for numerical solution of linear Ordinary Differential Equations (ODEs) and linear Differential-Algebraic Equations (DAEs). First we consider ODEs with some ordinary problems, and then, focus on those problems in which the solution function or some coefficient functions have singularities. Then, by expressing weak and strong aspects of spectral methods to solve these kinds of problems, a modified pseudospectral method which is more efficient than other spectral methods is suggested and tested on some examples. We extend the pseudo-spectral method to solve a system of linear ODEs and linear DAEs and compare this method with other methods such as Backward Difference Formulae (BDF), and implicit Runge-Kutta (RK) methods using some numerical examples. Furthermore, by using appropriatec hoice of Gauss-Chebyshev-Radapuo ints, we will show that this method can be used to solve a linear DAE whenever some of coefficient functions have singularities by providing some examples. We also used some problems that have already been considered by some authors by finite difference methods, and compare their results with ours. Finally, we present a short survey of properties and numerical methods for solving DAE problems and then we extend the pseudo-spectral method to solve DAE problems with variable coefficient functions. Our numerical experience shows that spectral and pseudo-spectral methods and their modified versions are very promising for linear ODE and linear DAE problems with solution or coefficient functions having singularities. In section 3.2, a modified method for solving an ODE is introduced which is new work. Furthermore, an extension of this method for solving a DAE or system of ODEs which has been explained in section 4.6 of chapter four is also a new idea and has not been done by anyone previously. In all chapters, wherever we talk about ODE or DAE we mean linear.

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Postell, Floyd Vince. "High order finite difference methods." Diss., Georgia Institute of Technology, 1990. http://hdl.handle.net/1853/28876.

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Banerjee, Paromita. "Numerical Methods for Stochastic Differential Equations and Postintervention in Structural Equation Models." Case Western Reserve University School of Graduate Studies / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=case1597879378514956.

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Handari, Bevina D. "Numerical methods for SDEs and their dynamics /." [St. Lucia, Qld.], 2002. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe17145.pdf.

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Khanamiryan, Marianna. "Numerical methods for systems of highly oscillatory ordinary differential equations." Thesis, University of Cambridge, 2010. https://www.repository.cam.ac.uk/handle/1810/226323.

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This thesis presents methods for efficient numerical approximation of linear and non-linear systems of highly oscillatory ordinary differential equations. Phenomena of high oscillation is considered a major computational problem occurring in Fourier analysis, computational harmonic analysis, quantum mechanics, electrodynamics and fluid dynamics. Classical methods based on Gaussian quadrature fail to approximate oscillatory integrals. In this work we introduce numerical methods which share the remarkable feature that the accuracy of approximation improves as the frequency of oscillation increases. Asymptotically, our methods depend on inverse powers of the frequency of oscillation, turning the major computational problem into an advantage. Evolving ideas from the stationary phase method, we first apply the asymptotic method to solve highly oscillatory linear systems of differential equations. The asymptotic method provides a background for our next, the Filon-type method, which is highly accurate and requires computation of moments. We also introduce two novel methods. The first method, we call it the FM method, is a combination of Magnus approach and the Filon-type method, to solve matrix exponential. The second method, we call it the WRF method, a combination of the Filon-type method and the waveform relaxation methods, for solving highly oscillatory non-linear systems. Finally, completing the theory, we show that the Filon-type method can be replaced by a less accurate but moment free Levin-type method.

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Djidjeli, Kamel. "Numerical methods for some time-dependent partial differential equations." Thesis, Brunel University, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.293104.

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Gyurko, Lajos Gergely. "Numerical methods for approximating solutions to rough differential equations." Thesis, University of Oxford, 2008. http://ora.ox.ac.uk/objects/uuid:d977be17-76c6-46d6-8691-6d3b7bd51f7a.

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The main motivation behind writing this thesis was to construct numerical methods to approximate solutions to differential equations driven by rough paths, where the solution is considered in the rough path-sense. Rough paths of inhomogeneous degree of smoothness as driving noise are considered. We also aimed to find applications of these numerical methods to stochastic differential equations. After sketching the core ideas of the Rough Paths Theory in Chapter 1, the versions of the core theorems corresponding to the inhomogeneous degree of smoothness case are stated and proved in Chapter 2 along with some auxiliary claims on the continuity of the solution in a certain sense, including an RDE-version of Gronwall's lemma. In Chapter 3, numerical schemes for approximating solutions to differential equations driven by rough paths of inhomogeneous degree of smoothness are constructed. We start with setting up some principles of approximations. Then a general class of local approximations is introduced. This class is used to construct global approximations by pasting together the local ones. A general sufficient condition on the local approximations implying global convergence is given and proved. The next step is to construct particular local approximations in finite dimensions based on solutions to ordinary differential equations derived locally and satisfying the sufficient condition for global convergence. These local approximations require strong conditions on the one-form defining the rough differential equation. Finally, we show that when the local ODE-based schemes are applied in combination with rough polynomial approximations, the conditions on the one-form can be weakened. In Chapter 4, the results of Gyurko & Lyons (2010) on path-wise approximation of solutions to stochastic differential equations are recalled and extended to the truncated signature level of the solution. Furthermore, some practical considerations related to the implementation of high order schemes are described. The effectiveness of the derived schemes is demonstrated on numerical examples. In Chapter 5, the background theory of the Kusuoka-Lyons-Victoir (KLV) family of weak approximations is recalled and linked to the results of Chapter 4. We highlight how the different versions of the KLV family are related. Finally, a numerical evaluation of the autonomous ODE-based versions of the family is carried out, focusing on SDEs in dimensions up to 4, using cubature formulas of different degrees and several high order numerical ODE solvers. We demonstrate the effectiveness and the occasional non-effectiveness of the numerical approximations in cases when the KLV family is used in its original version and also when used in combination with partial sampling methods (Monte-Carlo, TBBA) and Romberg extrapolation.

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Simpson, Arthur Charles. "Numerical methods for the solution of fractional differential equations." Thesis, University of Liverpool, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.250281.

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The fractional calculus is a generalisation of the calculus of Newton and Leibniz. The substitution of fractional differential operators in ordinary differential equations substantially increases their modelling power. Fractional differential operators set exciting new challenges to the computational mathematician because the computational cost of approximating fractional differential operators is of a much higher order than that necessary for approximating the operators of classical calculus. 1. We present a new formulation of the fractional integral. 2. We use this to develop a new method for reducing the computational cost of approximating the solution of a fractional differential equation. 3. This method can be implemented with two levels of sophistication. We compare their rates of convergence, their algorithmic complexity, and their weight set sizes so that an optimal choice, for a particular application, can be made. 4. We show how linear multiterm fractional differential equations can be approximated as systems of fractional differential equations of order at most 1.

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Books on the topic "Differential equations - Numerical methods"

1

Evans, Gwynne. Numerical methods for partial differential equations. London: Springer, 2000.

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Butcher, J. C. Numerical Methods for Ordinary Differential Equations. New York: John Wiley & Sons, Ltd., 2008.

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3

Numerical methods for partial differential equations. 3rd ed. Boston: Academic Press, 1992.

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4

Butcher, J. C. Numerical methods for ordinary differential equations. West Sussex: J. Wiley, 2002.

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5

Ascher, U. M. Numerical methods for evolutionary differential equations. Philadelphia: Society for Industrial and Applied Mathematics, 2008.

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Marino, Zennaro, ed. Numerical methods for delay differential equations. Oxford: Clarendon Press, 2003.

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Butcher, J. C. Numerical Methods for Ordinary Differential Equations. Chichester, UK: John Wiley & Sons, Ltd, 2016. http://dx.doi.org/10.1002/9781119121534.

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Butcher, J. C. Numerical Methods for Ordinary Differential Equations. Chichester, UK: John Wiley & Sons, Ltd, 2003. http://dx.doi.org/10.1002/0470868279.

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9

Griffiths, David F., and Desmond J. Higham. Numerical Methods for Ordinary Differential Equations. London: Springer London, 2010. http://dx.doi.org/10.1007/978-0-85729-148-6.

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Bellen, Alfredo, Charles W. Gear, and Elvira Russo, eds. Numerical Methods for Ordinary Differential Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/bfb0089227.

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Book chapters on the topic "Differential equations - Numerical methods"

1

Goodwine, Bill. "Numerical Methods." In Engineering Differential Equations, 577–630. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-7919-3_12.

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2

Cohen, Harold. "Partial Differential Equations." In Numerical Approximation Methods, 315–82. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-9837-8_8.

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Struthers, Allan, and Merle Potter. "Numerical Methods for Differential Equations." In Differential Equations, 373–407. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-20506-5_6.

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Gilbert, Robert P., George C. Hsiao, and Robert J. Ronkese. "Numerical Methods for First-Order Equations." In Differential Equations, 33–54. 2nd ed. Boca Raton: Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781003175643-3.

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5

Sobczyk, Kazimierz. "Stochastic Differential Equations: Numerical Methods." In Stochastic Differential Equations, 299–330. Dordrecht: Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3712-6_6.

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Davis, Jon H. "Introduction to Numerical Methods." In Differential Equations with Maple, 81–109. Boston, MA: Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-1376-5_4.

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Durran, Dale R. "Ordinary Differential Equations." In Numerical Methods for Fluid Dynamics, 35–87. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-6412-0_2.

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Cohen, Harold. "Ordinary First Order Differential Equations." In Numerical Approximation Methods, 237–68. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-9837-8_6.

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Cohen, Harold. "Ordinary Second Order Differential Equations." In Numerical Approximation Methods, 269–314. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-9837-8_7.

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Walter, Éric. "Solving Ordinary Differential Equations." In Numerical Methods and Optimization, 299–358. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-07671-3_12.

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Conference papers on the topic "Differential equations - Numerical methods"

1

Ying, Lungan, and Benyu Guo. "Numerical Methods for Partial Differential Equations." In Second Conference. WORLD SCIENTIFIC, 1992. http://dx.doi.org/10.1142/9789814537735.

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Aceto, Lidia, Cecilia Magherini, and Paolo Novati. "Generalized Adams methods for fractional differential equations." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756110.

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Wu, Xinyuan, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Symposium: Structure-Preserving Methods for Differential Equations." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2. AIP, 2009. http://dx.doi.org/10.1063/1.3241621.

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4

Chan, Robert P. K., Shixiao Wang, and Angela Y. J. Tsai. "Two-derivative Runge-Kutta methods for differential equations." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756113.

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Bougouffa, Smail, Saud Al-Awfi, Theodore E. Simos, and George Maroulis. "Numerical Treatment of Schrödinger Coupled Differential Equations." In COMPUTATIONAL METHODS IN SCIENCE AND ENGINEERING: Theory and Computation: Old Problems and New Challenges. Lectures Presented at the International Conference on Computational Methods in Science and Engineering 2007 (ICCMSE 2007): VOLUME 1. AIP, 2007. http://dx.doi.org/10.1063/1.2835951.

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Garrappa, Roberto. "A Comparison of Some Explicit Methods for Fractional Differential Equations." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2990895.

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Pedas, Arvet, Enn Tamme, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Piecewise Polynomial Collocation Methods for Fractional Differential Equations." In ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010. AIP, 2010. http://dx.doi.org/10.1063/1.3497889.

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Hrabovský, Juraj, Justín Murín, Mehdi Aminbaghai, Vladimír Kutiš, and Juraj Paulech. "NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS WITH NON-CONSTANT COEFFICIENTS." In VII European Congress on Computational Methods in Applied Sciences and Engineering. Athens: Institute of Structural Analysis and Antiseismic Research School of Civil Engineering National Technical University of Athens (NTUA) Greece, 2016. http://dx.doi.org/10.7712/100016.2153.6577.

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Komori, Yoshio. "Weak Order Drift‐implicit Runge‐Kutta Methods for Stochastic Differential Equations." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2990922.

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Akgül, Ali. "Some applications of novel numerical methods for differential equations." In CENTRAL EUROPEAN SYMPOSIUM ON THERMOPHYSICS 2019 (CEST). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5114232.

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Reports on the topic "Differential equations - Numerical methods"

1

Tewarson, Reginald P. Numerical Methods for Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, September 1986. http://dx.doi.org/10.21236/ada177283.

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Tewarson, Reginald P. Numerical Methods for Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, September 1985. http://dx.doi.org/10.21236/ada162722.

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Sharp, D. H., S. Habib, and M. B. Mineev. Numerical Methods for Stochastic Partial Differential Equations. Office of Scientific and Technical Information (OSTI), July 1999. http://dx.doi.org/10.2172/759177.

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Ewing, Richard E. Numerical and Analytical Methods in Nonlinear Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, April 1987. http://dx.doi.org/10.21236/ada185210.

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Werner, L., and F. Odeh. Numerical Methods for Stiff Ordinary and Elliptic Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, February 1985. http://dx.doi.org/10.21236/ada153247.

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Flaherty, Joseph E., and Robert E. O'Malley. Asymptotic and Numerical Methods for Singularly Perturbed Differential Equations with Applications to Impact Problems. Fort Belvoir, VA: Defense Technical Information Center, May 1986. http://dx.doi.org/10.21236/ada169251.

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Sharan, M., E. J. Kansa, and S. Gupta. Application of multiquadric method for numerical solution of elliptic partial differential equations. Office of Scientific and Technical Information (OSTI), January 1994. http://dx.doi.org/10.2172/10156506.

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Oliker, V. I., and P. Waltman. New Methods for Numerical Solution of One Class of Strongly Nonlinear Partial Differential Equations with Applications. Fort Belvoir, VA: Defense Technical Information Center, January 1986. http://dx.doi.org/10.21236/ada186166.

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Oliker, V. I., and P. Waltman. New Methods for Numerical Solution of One Class of Strongly Nonlinear Partial Differential Equations with Applications. Fort Belvoir, VA: Defense Technical Information Center, August 1987. http://dx.doi.org/10.21236/ada189945.

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Mitchell, Jason W. Implementing Families of Implicit Chebyshev Methods with Exact Coefficients for the Numerical Integration of First- and Second-Order Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, May 2002. http://dx.doi.org/10.21236/ada404958.

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