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- W2100015279 abstract "A multiple infinite trigonometric cum polynomial series method for solving initial-boundary value problems governed by hyperbolic differential equations with variable coefficients is developed. The method proposed herein can be easily applied to a broad class of engineering systems including those cases where boundary conditions may vary with time. In the proposed mathematical technique, the solution form is assumed as a combination of infinite Fourier series and polynomial series of nth order, where n is the order of the differential equation. The coefficients of the polynomial series are obtained as functions of undetermined Fourier series coefficients by satisfying the initial-boundary conditions. The variable coefficients are expanded in appropriate half-range sine or cosine series. Insertion of the above Fourier-polynomial series solutions into the differential equation and application of orthogonality conditions leads to a linear summation equation which can be solved in open form. However, the authors have developed a closed-form series solution consisting of a highly efficient algorithm. The major advantage of this technique is the development of a solution algorithm, coupled with the multiple infinite trigonometric cum polynomial series solutions, leading to fast converging series solutions. A representative initial and boundary value problem governed by hyperbolic partial differential equations of variable coefficients is presented herein to demonstrate the efficiency and accuracy of the method." @default.
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- W2100015279 date "1987-01-01" @default.
- W2100015279 modified "2023-09-27" @default.
- W2100015279 title "A series solution algorithm for initial boundary-value problems with variable properties" @default.
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- W2100015279 doi "https://doi.org/10.1016/0045-7949(87)90006-x" @default.
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