Geodesic
A rapidly convergent approximation scheme for nonlinear autonomous and non-autonomous wave-like equations
Filomat, Tome 35 (2021) no. 10, p. 3501

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DOI

In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of exponential instead of an algebraic function of independent variables. As a consequence: i) the convergence of the series found to be faster than the same obtained by few other methods and ii) the exact analytic solution can be obtained from the first few terms of the series of the approximate solution, in cases the equation is integrable. The convergence of the sum of the successive correction terms has been established and an estimate of the error in the approximation has also been presented. The efficiency of the present method has been illustrated through some examples with a variety of nonlinear terms present in the equation
DOI : 10.2298/FIL2110501D
Classification : 74H10, 35C05;35C10;34A12;35A25
Keywords: Autonomous and non-autonomous wave-like equations, Rapidly convergent approximation scheme, Accurate approximate solution, Convergence analysis, Error estimate, Exact solution 
Prakash Kumar Das; M M Panja. A rapidly convergent approximation scheme for nonlinear autonomous and non-autonomous wave-like equations. Filomat, Tome 35 (2021) no. 10, p. 3501 . doi: 10.2298/FIL2110501D
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     title = {A rapidly convergent approximation scheme for nonlinear autonomous and non-autonomous wave-like equations},
     journal = {Filomat},
     pages = {3501 },
     year = {2021},
     volume = {35},
     number = {10},
     doi = {10.2298/FIL2110501D},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2110501D/}
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