Penerapan Skema Modulasi Stabil Pada Penyelesaian Persamaan Diferensial Bernoulli

Ali Yunus Rohedi

Abstract


Penyelesaian persamaan diferensial Bernoulli (PD Bernoulli) secara tradisi selalu dilakukan melalui prosedur linierisasi dengan menggunakan fungsi transformasi Bernoulli. Pada makalah ini diperkenalkan teknik baru penyelesaian PD Bernoulli tanpa melibatkan prosedur linierisasi, yang didasarkan pada penerapan skema modulasi stabil. Penerapan metode yang dinamakan SMT (Stable Modulation Technique) atau teknik modulasi stabil tersebut dimulai dengan memecah PD Bernoulli atas bagian linier dan taklinier, kemudian menuliskan solusi bagian takliniernya dalam bentuk fungsi termodulasi yang nilai awalnya disamping diperankan sebagai suku amplitudo (A) juga dimodulasikan di dalam fungsi fasa F(A). Solusi eksak PD Bernoulli diberikan dalam formula AF(A), yang diperoleh setelah menggantikan solusi bagian linier ke dalam nilai awal fungsi termodulasi solusi bagian takliniernya. Pada paper ini dicontohkan penggunaan SMT pada penyelesaian PD Bernoulli untuk model penyimpanan energi magnet di dalam induktor.

Keywords


teknik modulasi stabil; fungsi termodulasi; formula AF(A)

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DOI: http://dx.doi.org/10.12962/j24604682.v3i1.960

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