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Relevant bibliographies by topics / Numerical solution of partial differential equations

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Academic literature on the topic 'Numerical solution of partial differential equations'

Author: Grafiati

Published: 4 June 2021

Last updated: 18 February 2022

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Journal articles on the topic "Numerical solution of partial differential equations"

1

M.A.Mohamed, M. A. Mohamed. "Numerical Solution of Nonlinear Partial Differential Equation by Legendre Multiwavelet Method." International Journal of Scientific Research 3, no. 2 (June 1, 2012): 1–8. http://dx.doi.org/10.15373/22778179/feb2014/188.

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Maset, Stefano. "Numerical solution of retarded functional differential equations as partial differential equations." IFAC Proceedings Volumes 33, no. 23 (September 2000): 133–35. http://dx.doi.org/10.1016/s1474-6670(17)36930-6.

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Zhang, Zhao. "Numerical Analysis and Comparison of Gridless Partial Differential Equations." International Journal of Circuits, Systems and Signal Processing 15 (August 31, 2021): 1223–31. http://dx.doi.org/10.46300/9106.2021.15.133.

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In the field of science and engineering, partial differential equations play an important role in the process of transforming physical phenomena into mathematical models. Therefore, it is very important to get a numerical solution with high accuracy. In solving linear partial differential equations, meshless solution is a very important method. Based on this, we propose the numerical solution analysis and comparison of meshless partial differential equations (PDEs). It is found that the interaction between the numerical solutions of gridless PDEs is better, and the absolute error and relative error are lower, which proves the superiority of the numerical solutions of gridless PDEs

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Abhyankar, N. S., E. K. Hall, and S. V. Hanagud. "Chaotic Vibrations of Beams: Numerical Solution of Partial Differential Equations." Journal of Applied Mechanics 60, no. 1 (March 1, 1993): 167–74. http://dx.doi.org/10.1115/1.2900741.

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The objective of this paper is to examine the utility of direct, numerical solution procedures, such as finite difference or finite element methods, for partial differential equations in chaotic dynamics. In the past, procedures for solving such equations to detect chaos have utilized Galerkin approximations which reduce the partial differential equations to a set of truncated, nonlinear ordinary differential equations. This paper will demonstrate that a finite difference solution is equivalent to a Galerkin solution, and that the finite difference method is more powerful in that it may be applied to problems for which the Galerkin approximations would be difficult, if not impossible to use. In particular, a nonlinear partial differential equation which models a slender, Euler-Bernoulli beam in compression issolvedto investigate chaotic motions under periodic transverse forcing. The equation, cast as a system of firstorder partial differential equations is directly solved by an explicit finite difference scheme. The numerical solutions are shown to be the same as the solutions of an ordinary differential equation approximating the first mode vibration of the buckled beam. Then rigid stops of finite length are incorporated into the model to demonstrate a problem in which the Galerkin procedure is not applicable. The finite difference method, however, can be used to study the stop problem with prescribed restrictions over a selected subdomain of the beam. Results obtained are briefly discussed. The end result is a more general solution technique applicable to problems in chaotic dynamics.

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FALCONE, M. "NUMERICAL METHODS FOR DIFFERENTIAL GAMES BASED ON PARTIAL DIFFERENTIAL EQUATIONS." International Game Theory Review 08, no. 02 (June 2006): 231–72. http://dx.doi.org/10.1142/s0219198906000886.

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In this paper we present some numerical methods for the solution of two-persons zero-sum deterministic differential games. The methods are based on the dynamic programming approach. We first solve the Isaacs equation associated to the game to get an approximate value function and then we use it to reconstruct approximate optimal feedback controls and optimal trajectories. The approximation schemes also have an interesting control interpretation since the time-discrete scheme stems from a dynamic programming principle for the associated discrete time dynamical system. The general framework for convergence results to the value function is the theory of viscosity solutions. Numerical experiments are presented solving some classical pursuit-evasion games.

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Jokar, Sadegh, Volker Mehrmann, Marc E. Pfetsch, and Harry Yserentant. "Sparse approximate solution of partial differential equations." Applied Numerical Mathematics 60, no. 4 (April 2010): 452–72. http://dx.doi.org/10.1016/j.apnum.2009.10.003.

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T., V., and G. D. Smith. "Numerical Solution of Partial Differential Equations, Finite Difference Methods." Mathematics of Computation 48, no. 178 (April 1987): 834. http://dx.doi.org/10.2307/2007849.

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Iserles, A., and G. D. Smith. "Numerical Solution of Partial Differential Equations: Finite Difference Methods." Mathematical Gazette 70, no. 454 (December 1986): 330. http://dx.doi.org/10.2307/3616228.

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Vanani, Solat, and Azim Aminataei. "On the Numerical Solution of Fractional Partial Differential Equations." Mathematical and Computational Applications 17, no. 2 (August 1, 2012): 140–51. http://dx.doi.org/10.3390/mca17020140.

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Soliman, A. F., A. M. A. EL-ASYED, and M. S. El-Azab. "On The Numerical Solution of Partial integro-differential equations." Mathematical Sciences Letters 1, no. 1 (May 1, 2012): 71–80. http://dx.doi.org/10.12785/msl/010109.

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Dissertations / Theses on the topic "Numerical solution of partial differential equations"

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Williamson, Rosemary Anne. "Numerical solution of hyperbolic partial differential equations." Thesis, University of Cambridge, 1985. https://www.repository.cam.ac.uk/handle/1810/278503.

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Tråsdahl, Øystein. "Numerical solution of partial differential equations in time-dependent domains." Thesis, Norwegian University of Science and Technology, Department of Mathematical Sciences, 2008. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-9752.

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Numerical solution of heat transfer and fluid flow problems in two spatial dimensions is studied. An arbitrary Lagrangian-Eulerian (ALE) formulation of the governing equations is applied to handle time-dependent geometries. A Legendre spectral method is used for the spatial discretization, and the temporal discretization is done with a semi-implicit multi-step method. The Stefan problem, a convection-diffusion boundary value problem modeling phase transition, makes for some interesting model problems. One problem is solved numerically to obtain first, second and third order convergence in time, and another numerical example is used to illustrate the difficulties that may arise with distribution of computational grid points in moving boundary problems. Strategies to maintain a favorable grid configuration for some particular geometries are presented. The Navier-Stokes equations are more complex and introduce new challenges not encountered in the convection-diffusion problems. They are studied in detail by considering different simplifications. Some numerical examples in static domains are presented to verify exponential convergence in space and second order convergence in time. A preconditioning technique for the unsteady Stokes problem with Dirichlet boundary conditions is presented and tested numerically. Free surface conditions are then introduced and studied numerically in a model of a droplet. The fluid is modeled first as Stokes flow, then Navier-Stokes flow, and the difference in the models is clearly visible in the numerical results. Finally, an interesting problem with non-constant surface tension is studied numerically.

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Ibrahem, Abdul Nabi Ismail. "The numerical solution of partial differential equations on unbounded domains." Thesis, Keele University, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.279648.

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Bratsos, A. G. "Numerical solutions of nonlinear partial differential equations." Thesis, Brunel University, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.332806.

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Sundqvist, Per. "Numerical Computations with Fundamental Solutions." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-5757.

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Pun, K. S. "The numerical solution of partial differential equations with the Tau method." Thesis, Imperial College London, 1985. http://hdl.handle.net/10044/1/37823.

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Pratt, P. "Problem solving environments for the numerical solution of partial differential equations." Thesis, University of Leeds, 1996. http://etheses.whiterose.ac.uk/1267/.

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The complexity and sophistication of numerical codes for the simulation of complex problems modelled by partial differential equations (PDEs) has increased greatly over the last decade. This makes it difficult for those without direct knowledge of the PDE software to employ it efficiently. Problem Solving Environments (PSEs) are seen as a way of making it possible to provide an easy-to-use layer surrounding the numerical software. The users can then concentrate on gaining an understanding of the physical problem through the results the code is providing. PSEs aim to aid novice and expert users in the problem specification process and to provide a natural way to solve the problem. They also decrease the time spent on the problem solving process. This study is concerned with the construction of a PSE for the numerical solution of PDEs. This is one area where PSEs can be used to particularly good effect because the solution process is complicated and error prone. The driving of numerical software and the construction of mathematical models used by the software pose problems for users of the software. The interpretation of results provided by the numerical code may also be difficult. It will be shown how PSEs can remedy these issues by allowing the user to easily specify and solve the problem. The construction of a prototype PSE is achieved through the utilisation and integration of existing scientific software tools and systems. An examination of the solution process of PDEs is used to identify the various components required in a PSE for such problems. The PSE makes use of an open design environment and incorporates the knowledge of the users and developers of the numerical code together with a set of generic software tools based on emerging standards. This combination of tools allows the PSE to automate the solution procedure for a number of PDE problems. Finally, the success of this approach to building PSEs is examined by reference to an engineering PDE problem.

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Barreira, Maria Raquel. "Numerical solution of non-linear partial differential equations on triangulated surfaces." Thesis, University of Sussex, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.496863.

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This work aims to solve numerically non-linear partial differential equations on surfaces, that may evolve in time, for a set of different applications. The core of all the numerical schemes is a finite element method recently introduced for triangulated surfaces. The main classes of applications under appreciation are the motion of curves on surfaces, segmentation of images painted on surfaces and the formation of Turing patterns on surfaces. For the first one, three different approaches are considered and compared: the level set method, the phase field framework and the diffusion generated motion method. The formation of patterns leads to an interesting application to the growth of tumours which is also investigated. Implementation of all numerical schemes proposed is carried out and some analysis on the convergence and stability of the approximations is presented. The finite element method has shown efficiency and great flexibility when it comes to the equations it can approximate and the surfaces it can handle.

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Qiao, Zhonghua. "Numerical solution for nonlinear Poisson-Boltzmann equations and numerical simulations for spike dynamics." HKBU Institutional Repository, 2006. http://repository.hkbu.edu.hk/etd_ra/727.

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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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Books on the topic "Numerical solution of partial differential equations"

1

Morton, K. W. Numerical solution of partial differential equations. New York: Cambridge University Press, 1994.

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1931-, Mayers D. F., ed. Numerical solution of partial differential equations. 2nd ed. Cambridge: Cambridge Univeristy Press, 2005.

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3

Bjørstad, Petter. Parallel Solution of Partial Differential Equations. New York, NY: Springer New York, 2000.

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4

W, Thomas J. Numerical partial differential equations. New York: Springer, 1995.

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5

Numerical solution of hyperbolic partial differential equations. Cambridge: Cambridge University Press, 2009.

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Trangenstein, J. A. Numerical solution of hyperbolic partial differential equations. Cambridge: Cambridge University Press, 2009.

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Partial differential equations: Analytical solution techniques. Pacific Grove, Calif: Wadsworth & Brooks/Cole Advanced Books & Software, 1990.

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8

Solution techniques for elementary partial differential equations. 2nd ed. Boca Raton, FL: Chapman & Hall/CRC, 2010.

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Solution techniques for elementary partial differential equations. Boca Raton: CRC Press, Taylor & Francis Group, 2016.

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1931-, Mayers D. F., ed. Numerical solution of partial differential equations: An introduction. Cambridge: Cambridge University Press, 1994.

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Book chapters on the topic "Numerical solution of partial differential equations"

1

Logan, J. David. "Numerical Computation of Solutions." In Applied Partial Differential Equations, 257–77. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-12493-3_6.

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Dean, Edward J., and Roland Glowinski. "On the Numerical Solution of the Elliptic Monge—Ampère Equation in Dimension Two: A Least-Squares Approach." In Partial Differential Equations, 43–63. Dordrecht: Springer Netherlands, 2008. http://dx.doi.org/10.1007/978-1-4020-8758-5_3.

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Bleecker, David, and George Csordas. "Numerical Solutions of PDEs — An Introduction." In Basic Partial Differential Equations, 503–58. Boston, MA: Springer US, 1992. http://dx.doi.org/10.1007/978-1-4684-1434-9_8.

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Pettersson, Mass Per, Gianluca Iaccarino, and Jan Nordström. "Numerical Solution of Hyperbolic Problems." In Polynomial Chaos Methods for Hyperbolic Partial Differential Equations, 31–44. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-10714-1_4.

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Ray, Santanu Saha, and Arun Kumar Gupta. "Numerical Solution of a System of Partial Differential Equations." In Wavelet Methods for Solving Partial Differential Equations and Fractional Differential Equations, 63–88. Boca Raton : CRC Press, 2018.: Chapman and Hall/CRC, 2018. http://dx.doi.org/10.1201/9781315167183-3.

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Stroud, K. A., and Dexter Booth. "Numerical solutions of partial differential equations." In Advanced Engineering Mathematics, 593–641. London: Macmillan Education UK, 2011. http://dx.doi.org/10.1057/978-0-230-34474-7_18.

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Saha Ray, Santanu. "Numerical Solutions of Partial Differential Equations." In Numerical Analysis with Algorithms and Programming, 591–640. Boca Raton : Taylor & Francis, 2016. | “A CRC title.”: Chapman and Hall/CRC, 2018. http://dx.doi.org/10.1201/9781315369174-10.

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Ray, Santanu Saha, and Arun Kumar Gupta. "Numerical Solution of Partial Differential Equations by Haar Wavelet Method." In Wavelet Methods for Solving Partial Differential Equations and Fractional Differential Equations, 23–62. Boca Raton : CRC Press, 2018.: Chapman and Hall/CRC, 2018. http://dx.doi.org/10.1201/9781315167183-2.

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Theting, Thomas Gorm. "Numerical Solution of Wick-Stochastic Partial Differential Equations." In Proceedings of the International Conference on Stochastic Analysis and Applications, 303–49. Dordrecht: Springer Netherlands, 2004. http://dx.doi.org/10.1007/978-1-4020-2468-9_18.

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Biner, S. Bulent. "Introduction to Numerical Solution of Partial Differential Equations." In Programming Phase-Field Modeling, 9–11. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-41196-5_2.

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Conference papers on the topic "Numerical solution of partial differential equations"

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Barletti, Luigi, Luigi Brugnano, Gianluca Frasca Caccia, and Felice Iavernaro. "Recent advances in the numerical solution of Hamiltonian partial differential equations." In NUMERICAL COMPUTATIONS: THEORY AND ALGORITHMS (NUMTA–2016): Proceedings of the 2nd International Conference “Numerical Computations: Theory and Algorithms”. Author(s), 2016. http://dx.doi.org/10.1063/1.4965308.

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Nunez, Rafael, Juan Gonzalez, and Jose Camberos. "Large-Scale Numerical Solution of Partial Differential Equations with Reconfigurable Computing." In 18th AIAA Computational Fluid Dynamics Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2007. http://dx.doi.org/10.2514/6.2007-4085.

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Campagna, R., S. Cuomo, S. Leveque, G. Toraldo, F. Giannino, and G. Severino. "Some remarks on the numerical solution of parabolic partial differential equations." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING 2017 (ICCMSE-2017). Author(s), 2017. http://dx.doi.org/10.1063/1.5012378.

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Rababah, Abedallah. "Numerical solution of Burger-Huxley second order partial differential equations using splines." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0027712.

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Corveleyn, Samuel, Stefan Vandewalle, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Component Reuse in Iterative Solvers for the Solution of Fuzzy Partial 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/10.1063/1.3241494.

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Gupta, Murli M. "Preface of the "Minisymposium on high accuracy solution of ordinary and partial differential equations"." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756338.

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Burg, Clarence, and Taylor Erwin. "Application of Richardson Extrapolation to the Numerical Solution of Partial Differential Equations." In 19th AIAA Computational Fluid Dynamics. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2009. http://dx.doi.org/10.2514/6.2009-3653.

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Sutherland, James C., and Tony Saad. "The Discrete Operator Approach to the Numerical Solution of Partial Differential Equations." In 20th AIAA Computational Fluid Dynamics Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2011. http://dx.doi.org/10.2514/6.2011-3377.

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"Study on the Numerical Solution and Application of Fractional Partial Differential Equations." In 2020 5th International Conference on Technologies in Manufacturing, Information and Computing. Francis Academic Press, 2020. http://dx.doi.org/10.25236/ictmic.2020.015.

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Siddique, Mohammad, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Symposium: Advances in the Numerical Solutions of Partial Differential Equations." In ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010. AIP, 2010. http://dx.doi.org/10.1063/1.3498011.

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Reports on the topic "Numerical solution of partial differential equations"

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Levine, Howard A. Numerical Solution of Ill Posed Problems in Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, September 1987. http://dx.doi.org/10.21236/ada189383.

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Levine, Howard A. Numerical Solution of I11 Posed Problems in Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, November 1985. http://dx.doi.org/10.21236/ada162378.

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Levine, Howard A. Numerical Solution of Ill Posed Problems in Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, April 1985. http://dx.doi.org/10.21236/ada166096.

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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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Dupont, Todd F. Some Investigations into Variable Meshes for Numerical Solution of Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, May 1986. http://dx.doi.org/10.21236/ada168977.

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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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Trenchea, Catalin. Efficient Numerical Approximations of Tracking Statistical Quantities of Interest From the Solution of High-Dimensional Stochastic Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, February 2012. http://dx.doi.org/10.21236/ada567709.

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Trenchea, Catalin. Efficient Numerical Approximations of Tracking Statistical Quantities of Interest From the Solution of High-Dimensional Stochastic Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, February 2012. http://dx.doi.org/10.21236/ada577122.

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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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