?url_ver=Z39.88-2004&rft_id=1517031083&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=APLIKASI+METODE+DEKOMPOSISI+ADOMIAN+PADA+PENYELESAIAN+SISTEM+PERSAMAAN+DIFERENSIAL+PARSIAL+LINIER+HOMOGEN+ORDE+1&rft.creator=++GALEH++WICAKSONO%2C+1517031083&rft.subject=500+ilmu+pengetahuan+alam+dan+matematika&rft.subject=510+Matematika&rft.description=Metode+Dekomposisi+Adomian+telah+banyak+digunakan+pada+penyelesaian+model-model+matematika+dalam+bentuk+persamaan+diferensial+baik+Persamaan+Diferensial+Biasa+(PDB)+maupun+Persamaan+Diferensial+Parsial+(PDP).+Metode+Dekomposisi+Adomian+terbagi+menjadi+tiga+langkah+inti.+Pertama++mendekomposisikan+bagian+F+dari+persamaan+operator++Fu(x%2Ct)%3Dg(x)+menjadi+R+dan+L+dengan+L+merupakan+operator+linier+yang+mempunyai+invers+L%5E(-1)+dan+R+merupakan+operator+linier+lainnya.+Langkah+yang+kedua+yaitu+dengan+mengoperasikan+operator+L%5E(-1)+pada+persamaan+tersebut+sehingga+didapatkan+u(x%2Ct)+dan+yang+ketiga+mengasumsikan+solusi+yang+diperoleh+pada+langkah+kedua+adalah+berbentuk+u(x%2Ct)%3D%E2%88%91_(n%3D0)%5E%E2%88%9E%E2%96%92%E3%80%96u_n+(x%2Ct)+%E3%80%97%2C+yang+memberikan+relasi+rekursif+dan+menyelesaikannya.+Berdasarkan+hasil+relasi+rekursif+diperoleh+solusi+u_i+untuk+i%3D0%2C1%2C2%2C3%2C%E2%80%A6++sehingga+solusi+penyelesaiannya+berbentuk+deret.+Pada+penelitian+ini%2C+Metode+Dekomposisi+Adomian+diterapkan+pada+masalah+nilai+awal+persamaan+diferensial+parsial+linier+homogen+orde+satu.+Dari+perbandingan+solusi+eksak+dengan+hasil+solusi+yang+diperoleh+menunjukan+bahwa+Metode+Dekomposisi+Adomian+memberikan+hasil+yang+sama+dengan+solusi+eksaknya.%0D%0A%0D%0A%0D%0A%0D%0AThe+Adomian+Decomposition+Method+has+been+widely+used+in+solving+mathematical+models+in+the+form+of+differential+equations%2C+both+Ordinary+Differential+Equations+(PDB)+and+Partial+Differential+Equations+(PDP).+The+Adomian+Decomposition+Method+is+divided+into+three+core+steps.+First+decompose+the+parts+F+of+the+operator+equation+Fu(x%2Ct)%3Dg(x)+into+L+and+R+where+L+is+a+linear+operator+that+has+an+inverse+L%5E(-1)+and+R+is+another+linear+operator.+the+second+step+is+to+operate+the+L%5E(-1)+in+this+equation+to+get+u(x%2Ct)++and+the+third+assumes+the+solution+obtained+in+the+second+step+is+of+form+u(x%2Ct)%3D%E2%88%91_(n%3D0)%5E%E2%88%9E%E2%96%92%E3%80%96u_n+(x%2Ct)+%E3%80%97+which+provides+a+recursive+relation+and+resolves+it.+Based+on+the+results+of+the+recursive+relation%2C+the+u_i+solution+for+i%3D0%2C1%2C2%2C3%2C%E2%80%A6+so+that+the+solution+is+in+the+form+of+a+series.+In+this+study%2C+the+Adomian+Decomposition+Method+was+applied+to+the+initial+value+problem+of+a+first+order+homogeneous+linear+partial+differential+equation.+From+the+comparison+of+the+exact+solution+with+the+results+obtained%2C+it+shows+that+the+Adomian+Decomposition+Method+gives+the+same+results+as+the+exact+solution%0D%0A&rft.publisher=FAKULTAS+MATEMATIKA+DAN+ILMU+PENGETAHUAN+ALAM&rft.date=2022-02-21&rft.type=Skripsi&rft.type=NonPeerReviewed&rft.format=text&rft.identifier=http%3A%2F%2Fdigilib.unila.ac.id%2F63855%2F1%2FABSTRAK.pdf&rft.format=text&rft.identifier=http%3A%2F%2Fdigilib.unila.ac.id%2F63855%2F2%2FSKRIPSI%2520FULL.pdf&rft.format=text&rft.identifier=http%3A%2F%2Fdigilib.unila.ac.id%2F63855%2F3%2FSKRIPSI%2520FULL%2520TANPA%2520PEMBAHASAN.pdf&rft.identifier=+++GALEH+WICAKSONO%2C+1517031083++(2022)+APLIKASI+METODE+DEKOMPOSISI+ADOMIAN+PADA+PENYELESAIAN+SISTEM+PERSAMAAN+DIFERENSIAL+PARSIAL+LINIER+HOMOGEN+ORDE+1.++FAKULTAS+MATEMATIKA+DAN+ILMU+PENGETAHUAN+ALAM%2C+UNIVERSITAS+LAMPUNG.+++++&rft.relation=http%3A%2F%2Fdigilib.unila.ac.id%2F63855%2F