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Residual Power Series Method for Wave Type Equations
2021 International Conference on Applied and Engineering Mathematics (ICAEM), 2021In this article residual power series method (RPSM) is proposed for wave type partial differential equations (PDEs). This method is based on power series along with residual concept. RPSM is applied to test problem of wave type equation and results are analyzed through tables and figures at different time levels.
Mubashir Qayyum, Amna Khan
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Modified Residual Power Series Method for Boundary Value Problems
2021 International Conference on Applied and Engineering Mathematics (ICAEM), 2021In this manuscript, a new modification of residual power series method (RPSM) has been introduced for the solution of ordinary differential equations (ODEs) with boundary conditions. Proposed scheme has been applied to linear and nonlinear test problems of order two and four.
Mubashir Qayyum, Qursam Fatima
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Residual Power Series Method for Fractional Diffusion Equations
Fundamenta Informaticae, 2017In this article, improved residual power series method (RPSM) is effectively implemented to find the approximate analytical solution of a time fractional diffusion equations. The proposed method is an analytic technique based on the generalized Taylor’s series formula which construct an analytical solution in the form of a convergent series.
Kumar, Amit +2 more
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A New Algorithm of Residual Power Series (RPS) Technique
International Journal of Applied and Computational Mathematics, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Reversion of power series by residues
Communications in Algebra, 1998The Grothendieck residue map is used to reverse power series in a characteristic-free manner. An operator theoretic method for reversing power series is linked to the Grothendieck residue method by local duality.
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Power-Series, Residues, Singularities
2020The sequence \(\{t_n\}_{n=0}^\infty \subseteq \mathbb C\) is said to converge absolutely if there is a β > 0 such that for each positive integer n we have \(\sum _{p=1}^{n}|t_p-t_{p-1}| \leq \beta \).
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Residual Power Series Solution of Fractional bi-Hamiltonian Boussinesq System
2020In this paper, the residual power series method (RPSM) which is based on the generalized Taylor’s series formula has been used to investigate the approximated analytical solution for the fractional bi-Hamiltonian Boussinesq system. The solution of governing equation is calculated in the form of speedily convergent series.
Sachin Kumar, Baljinder Kour
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Analytical Solution of Fractional Burgers-Huxley Equations via Residual Power Series Method
Lobachevskii Journal of Mathematics, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Freihet, A. A., Zuriqat, M.
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Residual Power Series Approach for Solving Linear Fractional Swift-Hohenberg Problems
2020In this paper, a modified residual fractional power series technique is applied to provide an analytic-numeric approximated solution for linear time-fractional Swift-Hohenberg equation. The proposed algorithm relies on minimizing the residual error that results when approximating the solution by a truncated fractional Taylor series.
Shatha Hasan +3 more
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