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- 한국산업응용수학회 JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS Journal of the Korean Society for Industrial and Applied Mathematics Vol.26 No.4
- 발행연도
- 2022.12
- 수록면
- 185 - 223 (39page)
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The classical equation of Jonathan Homer Lane and Robert Emden, a nonlinear second-order ordinary differential equation, models the isothermal spherical clouded gases under the influence of the mutual attractive interaction between the gases’ molecules. In this paper, the Adomian decomposition method (ADM) is presented to obtain highly accurate and reliable analytical solutions of a class of generalised Lane-Emden equations with strong nonlinearities. The nonlinear term f(y(x)) of the proposed problem is given by the integer powers of a continuous real-valued function h(y(x)), that is, f(y(x)) = h<SUP>m</SUP>(y(x)), for integer m ≥ 0, real x > 0. In the end, numerical comparisons are presented between the analytical results obtained using the ADM and numerical solutions using the eighth-order nested second derivative two-step Runge-Kutta method (NSDTSRKM) to illustrate the reliability, accuracy, effectiveness and convenience of the proposed methods. The special cases h(y) = sin y(x), cos y(x); h(y) = sinh y(x), cosh y(x) are considered explicitly using both methods. Interestingly, in each of these methods, a unified result is presented for an integer power of any continuous real-valued function - compared with the case by case computations for the nonlinear functions f(y). The results presented in this paper are a generalisation of several published results. Several examples are given to illustrate the proposed methods. Tables of expansion coefficients of the series solutions of some special Lane-Emden type equations are presented. Comparisons of the two results indicate that both methods are reliably and accurately efficient in solving a class of singular strongly nonlinear ordinary differential equations.
목차
ABSTRACT
1. INTRODUCTION
2. ADOMIAN POLYNOMIALS FOR NONLINEAR FUNCTIONS
3. ANALYTICAL SOLUTION OF LANE-EMDEN TYPE PROBLEM USING ADOMIAN DECOMPOSITION METHOD
4. NESTED SECOND DERIVATIVE TWO-STEP RUNGE-KUTTA METHOD FOR SOLVING LANE-EMDEN TYPE PROBLEM
5. NUMERICAL RESULTS AND DISCUSSION
6. CONCLUDING REMARKS
REFERENCES
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UCI(KEPA) : I410-ECN-0101-2023-410-000318821