Numerisk l\303\270sning av ODEs%;Vi kan enkelt finne numeriske approksimasjoner til l\303\270sninger av forskjellige ordin\303\246re differensialligninger med Maple. Til dette bruker vi pakken Student[NumericalAnalysis]: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print(); # input placeholderVi pr\303\270ver oss p\303\245 f\303\270lgende ligning: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print(); # input placeholderFor \303\245 implementere en numerisk metode, bruker vi kommandoen InitialValueProblem(ligning, initialbetingelser, verdi, metode, undermetode):print(); # input 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(); # input placeholderHer har vi brukt initialverdien y(0)=0. Vi tiln\303\246rmer l\303\270sningen i x=2 og metoden vi bruker er Modified Euler (som er en Runge-Kutta-metode).Maple bruker 5 skritt om ikke annet er oppgitt. For \303\245 bruke noe annet, spesifiserer vi det med numsteps: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print(); # input placeholderKommandoen output= lar oss bestemme hva slags svar vi skal f\303\245. information gir en liste som du ser over. Vi kan ogs\303\245 f\303\245 et plot av l\303\270sningen. Under har vi benyttet Eulers metode: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%;LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=