1. Adaptive backward Euler time stepping with truncation error control for numerical modelling of unsaturated fluid flow.  
   Kavetski, Dmitri; Binning, Philip; Sloan, Scott W.   
   Internat. J. Numer. Methods Engrg. 53 (2002), no. 6, 1301--1322, MathSciNet.  
2. The Euler method in the numerical integration of reaction-diffusion problems with blow-up.  
   Abia, L. M.; López-Marcos, J. C.; Martínez, J.  
   Appl. Numer. Math. 38 (2001), no. 3, 287--313, MathSciNet.  
3. Periodic orbits in the Euler method for a class of delay differential equations  
   Koto, T.  
   Computers and Mathematics With Applications, 2001, vol. 42, no. ER12, pp. 1597-1608, Ingenta.  
4. The composite Euler method for stiff stochastic differential equations  
   Burrage, K.; Tian, T.  
   Journal of Computational and Applied Mathematics, 2001, vol. 131, no. ER1-2, pp. 407-426, Ingenta.  
5. A note on the stability properties of the Euler methods for solving stochastic differential equations  
   Burrage, Kevin; Tian, Tianhai  
   Dedicated to John Butcher. New Zealand J. Math. 29 (2000), no. 2, 115--127, MathSciNet.   
6. The implicit Euler method for the numerical solution of singular initial value problems  
   Koch, Othmar; Kofler, Peter; Weinmüller, Ewa B.  
   Auckland numerical ordinary differential equations (Auckland, 1998). Appl. Numer. Math. 34 (2000), no. 2-3, 231--252, MathSciNet.  
7. On the method of modified equations. IV. Numerical techniques based on the modified equation for the Euler forward difference method.  
   Villatoro, F. R.; Ramos, J. I.  
   Appl. Math. Comput. 103 (1999), no. 2-3, 213--240, MathSciNet.  
8. On the method of modified equations. III. Numerical techniques based on the second equivalent equation for the Euler forward difference method.  
   Villatoro, F. R.; Ramos, J. I.  
   Appl. Math. Comput. 103 (1999), no. 2-3, 179--212, MathSciNet.  
9. On the method of modified equations. II. Numerical techniques based on the equivalent equation for the Euler forward difference method.  
   Villatoro, F. R.; Ramos, J. I.  
   Appl. Math. Comput. 103 (1999), no. 2-3, 141--177, MathSciNet.  
10. On the method of modified equations. I: Asymptotic analysis of the Euler forward difference method.  
    Villatoro, F.R.; Ramos, J.I.  
    Applied mathematics and computation, 1999, vol. 103, no. 2/3, pp. 111 , MathSciNet.  
11. Inequalities of moderate deviation type in the Euler method for stochastic differential equations: the example of the geometric Brownian motion  
    Clement, Emmanuelle
    Stochastics Stochastics Rep. 67 (1999), no. 3-4, 287--307, MathSciNet.   
12. Naimark-Sacker bifurcations in the Euler method for a delay differential equation  
    Koto, T.
    BIT 39 (1999), no. 1, 110--115, MathSciNet.   
13. Backward Euler method for abstract time-dependent parabolic equations with variable domains  
    Palencia, C.
    Numer. Math. 82 (1999), no. 3, 471--490, MathSciNet.   
14. Numerical stability of implicit Euler methods for pantograph differential equations. (Chinese)  
    Wen, Li Ping  
    J. Changsha Univ. Electr. Power Nat. Sci. Ed. 14 (1999), no. 1, 10--12, MathSciNet.  
15. A comparison of numerical ODE solvers based on Euler methods.  
    Inç, Mustafa; Bildik, Necdet; Bulut, Hasan  
    Math. Comput. Appl. 3 (1998), no. 3, 153--159, MathSciNet.  
16. On the backward Euler method for time dependent parabolic integro-differential equations with nonsmooth initial data  
    Pani, Amiya K.; Sinha, Rajen K.
    J. Integral Equations Appl. 10 (1998), no. 2, 219--249, MathSciNet.   
17. Weak consistency of the Euler method for numerically solving stochastic differential equations with discontinuous coefficients  
    Chan, K. S.; Stramer, O.
    Stochastic Process. Appl. 76 (1998), no. 1, 33--44, MathSciNet.   
18. Stability of the implicit Euler method for nonlinear systems of multidelay differential equations. (Chinese)  
    Zhang, Cheng Jian
    Hunan Daxue Xuebao 25 (1998), no. 1, 1--4, MathSciNet.   
19. Asymptotic error distributions for the Euler method for stochastic differential equations  
    Jacod, Jean; Protter, Philip
    Ann. Probab. 26 (1998), no. 1, 267--307, MathSciNet.   
20. A note on asymptotic properties of the estimator derived from the Euler method for diffusion processes at discrete times  
    Shoji, Isao
    Statist. Probab. Lett. 36 (1997), no. 2, 153--159, MathSciNet.   
21. Euler method vs. Gess method for dynamical systems  
    Yu, Dong Won
    Korean J. Comput. Appl. Math. 4 (1997), no. 2, 337--345, MathSciNet.   
22. Euler's method revisited  
    Lempio, F.
    Trudy Mat. Inst. Steklov. 211 (1995), Optim. Upr. i Differ. Uravn., 473--494, MathSciNet.   
23. The dynamics of the linearized implicit Euler method in solving ordinary differential equations
    Arriola, Leon
    Proceedings of the First International Conference on Difference Equations (San Antonio, TX, 1994), 29--39, Gordon and Breach, Luxembourg, 1995, MathSciNet.   
24. A variance reduction technique for use with the extrapolated Euler method for numerical solution of stochastic differential equations  
    Goodlett, S. T.; Allen, E. J.
    Stochastic Anal. Appl. 12 (1994), no. 1, 131--140, MathSciNet.   
25. Mid-point Euler method in Fourier pseudospectral approximation for fluid flow with low Mach number. I.
    Rashid, Abdur  
    Shanghai Keji Daxue Xuebao 16 (1993), no. 4, 418--426, MathSciNet.   
26. Euler's method for a first order partial differential equation  
    Poorkarimi, H.
    Libertas Math. 13 (1993), 173--175, MathSciNet.   
27. Numerical solution of differential equations. I. Euler's method. (Slovenian)
    Orel, Bojan
    Obzornik Mat. Fiz. 39 (1992), no. 4, 105--111, MathSciNet.   
28. Convergence of the generalized implicit Euler method  
    Yu, Dong Won
    Bull. Korean Math. Soc. 29 (1992), no. 1, 31--40, MathSciNet.   
29. Efficient Newton-Raphson and implicit Euler methods for solving the HNC equation  
    Busigin, Anthony; Phillips, Colin R.
    Molecular Phys. 76 (1992), no. 1, 89--101, MathSciNet.   
30. Numerical solution of differential equations. I. Euler's method. (Slovenian)  
    Orel, Bojan  
    Obzornik Mat. Fiz. 39 (1992), no. 4, 105--111, MathSciNet.  
31. A Modified Euler Method for Dynamic Analyses.  
    Hahn, G.D.  
    International journal for numerical methods in e, 1991, vol. 32, no. 5, pp. 943 , Ingenta.  
32. Asymptotic Error Expansions for Stiff Equations: The Implicit Euler Scheme  
    W. Auzinger, R. Frank, F. Macsek  
    SIAM Journal on Numerical Analysis, Vol. 27, No. 1. (Feb., 1990), pp. 67-104, Jstor.  
33. The Backward Euler Method for Numerical Solution of the Hodgkin-Huxley Equations of Nerve Conduction
    Michael Mascagni  
    SIAM Journal on Numerical Analysis, Vol. 27, No. 4. (Aug., 1990), pp. 941-962, Jstor.  
34. Molecular dynamics by the backward-Euler method  
    Peskin, Charles S.; Schlick, Tamar
    Comm. Pure Appl. Math. 42 (1989), no. 7, 1001--1031, MathSciNet.   
35. On the application of the implicit "backward Euler" method for solving the diffusion equation.  
    Lehmann, R.  
    Atmospheric environment, 1989, vol. 23, no. 1, pp. 115 , Ingenta.  
36. On the convergence of Euler's method
    McKee, S.
    Bull. Inst. Math. Appl. 20 (1984), no. 7-8, 115--120, MathSciNet.   
37. Global error estimation in the numerical solution of integro-differential equations by Euler's method  
    Jackiewicz, Z.
    Zastos. Mat. 18 (1984), no. 3, 487--501, MathSciNet.   
38. Global error estimation in the numerical solution of retarded differential equations by Euler's method.  
    Jackiewicz, Zdzisaw  
    Apl. Mat. 28 (1983), no. 3, 177--185, MathSciNet.  
39. On the Backward Euler Method for Parabolic Equations with Rough Initial Data  
    Huang Mingyou, Vidar Thomee  
    SIAM Journal on Numerical Analysis, Vol. 19, No. 3. (Jun., 1982), pp. 599-603, Jstor.  
40. The Numerical Solution of Volterra Functional Differential Equations by Euler's Method  
    Colin W. Cryer, Lucio Tavernini  
    SIAM Journal on Numerical Analysis, Vol. 9, No. 1. (Mar., 1972), pp. 105-129, Jstor.   
41. The application of Euler's method of polygons to the numerical solution of linear integro-differential equations. (Russian)  
    Matrohin, B. A.  
    Trudy Naucn. Ob\cdprime ed. Prepodav. Fiz.-Mat. Fak. Ped. Inst. Dalprime n. Vostok. 5 1965 108--113, MathSciNet.  

(c) John H. Mathews 2003