Sains Malaysiana 51(6)(2022): 1905-1914

http://doi.org/10.17576/jsm-2022-5106-25

Approximate-Analytic Solution of Hyperchaotic Finance System by Multistage Approach

(Penyelesaian Analitik Anggaran Sistem Kewangan Hiperkalut Menggunakan Pendekatan Multitahap)

Y.M. RANGKUTI^1,*, A.K. ALOMARI², N.R. ANAKIRA³ & A.F. JAMEEL⁴

¹Mathematics Department, Faculty of Mathematics and Natural Science, Universitas Negeri Medan, 20221, Medan, North Sumatera, Indonesia

²Mathematics Department, Faculty of Science, Yarmouk University, 22110, Irbid, Jordan

³Department of Mathematics, Faculty of Science and Technology, Irbid National University, 2600 Irbid, Jordan

⁴School of Quantitative Sciences, Faculty of Science, Universiti Utara Malaysia (UUM), 06010 Sintok, Kedah Darul Aman, Malaysia

Received: 3 July 2021/Accepted: 30 November 2021

Abstract

This paper devotes to constructing an approximate analytic solution for the hyperchaotic finance model. The model describes the time variation of the interest rate, the investment demand, the price exponent, and the average profit margin. The multistage homotopy analysis method (MHAM) and multistage variational iteration method (MVIM) are utilized to generate the analytical solutions. The solutions are presented in terms of continuous piecewise functions without interpolation. These procedures prove their applicability for this kind of model due to rapidly convergent series solutions with easily computable terms, iterates, and efficiently obtained by applying it over multiple time intervals. We also provide the convergences theorem of the MHAM. Numerical comparisons are displayed with the results obtained by MHAM, MVIM, and the fourth-order Runge-Kutta method to demonstrate the validity and effectivity of this procedure.

Keywords: Finance system; hyperchaotic system; multistage homotopy analysis method; multistage variational iteration method

Abstrak

Kertas ini membincangkan pembinaan penyelesaian analitik anggaran bagi model kewangan hiperkalut. Model ini melibatkan variasi masa kadar faedah, permintaan pelaburan, eksponen harga dan margin untung purata. Kaedah analisis homotopi multitahap (KAHM) dan kaedah lelaran variasi multitahap (KLVM) dibina dan digunakan untuk mendapatkan penyelesaian yang berbentuk fungsi cebisan selanjar tanpa interpolasi. Kemampuan kedua-dua kaedah ini terbukti berhasil untuk model seperti ini kerana penyelesaian sirinya didapati cepat menumpu dan sebutan dalam penyelesaiannya mudah dihitung di dalam lelaran. Ketepatan penyelesaian dapat diperoleh melalui penerapannya dalam beberapa selang masa berganda. Kertas ini turut memperuntukkan teorem penumpuan KAHM. Perbandingan berangka bagi keputusan yang diperoleh daripada KAHM, KLVM dan kaedah Runge-Kutta peringkat keempat dipaparkan untuk menunjukkan kesahihan dan keberkesanan kedua-dua kaedah baharu ini.

Kata kunci: Kaedah analisis homotopi multitahap (KAHM); kaedah lelaran variasi multitahap (KLVM); sistem berkekalutan hiper; sistem kewangan

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^*Corresponding author; email: yulitamolliq@unimed.ac.id