Newton-Raphson linearization? Second-Order Nonlinear ODE numpy-scipy Python -

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मैं एक से अधिक सप्ताह को हल करने का प्रयास कर रहा हूं:

यहां छवि विवरण दर्ज करें

मुझे यू के अनुमानित समाधान प्राप्त करने के लिए न्यूटन-रैफसन पद्धति का उपयोग करना होगा। मुझे ऐसा करने की स्क्रिप्ट है, लेकिन मुझे इस गैर रेखीय ओडीई को "लाइनरीज़ करना" चाहिए। K1-k4 स्थिर नहीं हैं प्रत्येक ग्रिड बिंदु (एक्स = 1-100) पर उन्हें एक अलग मान मिलता है जो गणना की जाती है। प्रारंभिक स्थिति यू (0) = 0 है

क्या यह होमवर्क असाइनमेंट है?

इसके अलावा, यह सीमा मान समस्या है या एक ओडीई? आप जो लिखते हैं, यह बीवीपी की तरह लगता है इसके अलावा, u (0) पर आपकी सीमा की स्थिति पर्याप्त नहीं है।

यदि बीवीपी, आप बस का उपयोग कर सकते हैं या आपके लिए मुश्किल भागों को कर सकते हैं।

यदि ओडीई, समस्या को पहले ऑर्डर सिस्टम के रूप में लिखें, और scipy.integrate.odint या scipy.integrate.ode का उपयोग करें।

लाइनरिजनाइजेशन के बारे में (यह मानना ​​है कि यह एक बीवीपी है): व्यवहार में यह आमतौर पर संख्यात्मक भेदभाव के माध्यम से न्यूटन पद्धति के लिए अपेक्षित आंशिक व्युत्पत्ति की गणना करने के लिए पर्याप्त है।

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