Deeba, E.; Khuri, S. A.; Xie, Shishen An algorithm for solving a nonlinear integro-differential equation. (English) Zbl 1023.65152 Appl. Math. Comput. 115, No. 2-3, 123-131 (2000). Summary: An algorithm based on Adomian’s decomposition method is developed to approximate the solution of the nonlinear integro-differential equation \[ u_t(x,t)= \int^t_0 a(t-\tau) {\partial\over \partial x} \sigma\bigl(u_x (x,\tau)\bigr) d\tau+ f(x,t),\;0<x<1,\;0<t<T, \]\[ u(x,0)= \psi(x). \] Special cases of the integro-differential equation are solved using the algorithm. It turns out that the convergence of this algorithm is rapid. Cited in 22 Documents MSC: 65R20 Numerical methods for integral equations 45G10 Other nonlinear integral equations 45K05 Integro-partial differential equations Keywords:Adomian’s decomposition method; nonlinear integro-differential equation; algorithm; convergence PDFBibTeX XMLCite \textit{E. Deeba} et al., Appl. Math. Comput. 115, No. 2--3, 123--131 (2000; Zbl 1023.65152) Full Text: DOI References: [1] Adomian, G., A review of the decomposition method and some recent results for nonlinear equation, Math. Comput. Modelling, 13, 17-43 (1990) · Zbl 0713.65051 [2] Adomian, G., A new approach to the heat equation - An application of the decomposition method, J. Math. Anal. Appl., 113, 202-209 (1986) · Zbl 0606.35037 [3] Adomian, G., A new approach to nonlinear partial differential equations, J. Math. Anal. Appl., 102, 420-434 (1984) · Zbl 0554.60065 [4] Adomian, G., A review of the decomposition method and some recent results for nonlinear equations, Math. Comput. Modelling, 13, 17-43 (1990) · Zbl 0713.65051 [5] Cherruault, Y.; Saccomandi, G.; Some, B., New results for convergence of Adomian’s method applied to integral equations, Math. Comput. Modelling, 16, 85-93 (1992) · Zbl 0756.65083 [6] Coleman, B. D.; Gurtin, M. E., Waves in materials with memory II on the growth and decay of one-dimensional acceleration waves, Arch. Rational Mech. Anal., 19, 239-265 (1965) · Zbl 0244.73017 [7] Gurtin, M. E.; Pipkin, A. C., A general theory of heat conduction with finite wave speeds, Arch. Rational Mech. Anal., 31, 113-126 (1968) · Zbl 0164.12901 [8] Levin, J. J.; Nohel, J. A., Perturbations of a non-linear equation, Mich. Math. J., 12, 431-447 (1965) · Zbl 0139.29304 [9] MacCamy, R. C., An integro-dimensional, equation with application in heat flow, Quart. Appl. Math., 35, 1-19 (1997) · Zbl 0351.45018 [10] MacCamy, R. C., A model for one-dimensional, nonlinear viscoelasticity, Quart. Appl. Math., 35, 21-23 (1977) · Zbl 0355.73041 [11] Neta, B., Numerical solution of a nonlinear integro-differential equation, J. Math. Anal. Appl., 89, 598-611 (1982) · Zbl 0488.65074 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.