Excel实现四阶龙格库塔法(Runge-Kutta)解二阶常微分方程范例.xls

Excel实现四阶龙格库塔法(Runge-Kutta)解二阶常微分方程范例.xls

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hx解析解4RK解yv,yk1l10.010.0001.0000001.0000000.000000-2.0000000.0000000.010.0100.9998990.999899-0.020252-2.050554-0.0202520.010.0200.9995930.999593-0.041015-2.102231-0.0410150.010.0300.9990770.999077-0.062300-2.155055-0.0623000.010.0400.9983450.998345-0.084120-2.209050-0.0841200.010.0500.9973930.997393-0.106485-2.264242-0.1064850.010.0600.9962140.996214-0.129409-2.320654-0.1294090.010.0700.9948030.994803-0.152903-2.378313-0.1529030.010.0800.9931540.993154-0.176979-2.437246-0.1769790.010.0900.9912610.991261-0.201652-2.497478-0.2016520.010.1000.9891190.989119-0.226933-2.559037-0.2269330.010.1100.9867210.986721-0.252837-2.621952-0.2528370.010.1200.9840600.984060-0.279377-2.686251-0.2793770.010.1300.9811310.981131-0.306567-2.751962-0.3065670.010.1400.9779260.977926-0.334421-2.819116-0.3344210.010.1500.9744400.974440-0.362954-2.887742-0.3629540.010.1600.9706650.970665-0.392181-2.957872-0.3921810.010.1700.9665940.966594-0.422117-3.029538-0.4221170.010.1800.9622200.962220-0.452777-3.102771-0.4527770.010.1900.9575360.957536-0.484177-3.177604-0.4841770.010.2000.9525340.952534-0.516334-3.254071-0.5163340.010.2100.9472070.947207-0.549264-3.332207-0.5492640.010.2200.9415460.941546-0.582984-3.412045-0.5829840.010.2300.9355450.935545-0.617511-3.493622-0.6175110.010.2400.9291930.929193-0.652862-3.576974-0.6528620.010.2500.9224840.922484-0.689056-3.662138-0.6890560.010.2600.9154090.915409-0.726111-3.749153-0.7261110.010.2700.9079590.907959-0.764046-3.838056-0.7640460.010.2800.9001250.900125-0.802879-3.928888-0.8028790.010.2900.8918990.891899-0.842630-4.021688-0.8426300.010.3000.8832700.883270-0.883319-4.116498-0.8833190.010.3100.8742290.874229-0.924967-4.213359-0.9249670.010.3200.8647670.864767-0.967594-4.312315-0.9675940.010.3300.8548740.854874-1.011220-4.413409-1.0112200.010.3400.8445390.844539-1.055869-4.516686-1.0558690.010.3500.8337530.833753-1.101562-4.622191-1.1015620.010.3600.8225050.822505-1.148320-4.729970-1.1483200.010.3700.8107830.810783-1.196169-4.840072-1.1961690.010.3800.7985770.798577-1.245130-4.952544-1.2451300.010.3900.7858770.785877-1.295228-5.067436-1.2952280.010.4000.7726690.772669-1.346487-5.184798-1.3464870.010.4100.7589430.758943-1.398932-5.304682-1.3989320.010.4200.7446860.744686-1.452589-5.427139-1.4525890.010.4300.7298870.729887-1.507484-5.552225-1.5074840.010.4400.7145320.714532-1.563642-5.679992-1.5636420.010.4500.6986100.698610-1.621092-5.810497-1.6210924RK与解析解对比0.6000.5000.4000.3000.2000.1000.0000.4000000.5000000.6000000.7000000.8000000.9000001.0000001.100000解析解4RK解y0.010.4600.6821060.682106-1.679862-5.943797-1.6798620.010.4700.6650080.665008-1.739978-6.079950-1.7399780.010.4800.6473020.647302-1.801470-6.219015-1.8014700.010.4900.6289740.628974-1.864368-6.361052-1.8643680.010.5000.6100100.610010-1.928701-6.506124-1.928701k2l2k3l3k4l4-2.025000-0.010000-2.025275-0.010125-2.050556-0.020253-2.076110-0.030505-2.076390-0.030632-2.102233-0.041016-2.128354-0.051526-2.128641-0.051657-2.155057-0.062301-2.181758-0.073076-2.182051-0.073209-2.209052-0.084121-2.236345-0.095165-2.236644-0.095302-2.264244-0.106486-2.292140-0.117806-2.292446-0.117946-2.320656-0.129410-2.349170-0.141012-2.349481-0.141155-2.378315-0.152904-2.407459-0.164794-2.407777-0.164940-2.437248-0.176980-2.467034-0.189165-2.467359-0.189314-2.497480-0.201653-2.527923-0.214139-2.528255-0.214291-2.559040-0.226934-2.590154-0.239728-2.590492-0.239884-2.621954-0.252838-2.653753-0.265947-2.654099-0.266106-2.686253-0.279378-2.718751-0.292808-2.719104-0.292971-2.751964-0.306568-2.785176-0.320327-2.785536-0.320493-2.819118-0.334422-2.853058-0.348516-2.853426-0.348686-2.887745-0.362955-2.922429-0.377393-2.922805-0.377566-2.957875-0.392182-2.993319-0.406970-2.993702-0.407147-3.029541-0.422118-3.065760-0.437264-3.066152-0.437445-3.102774-0.452778-3.139785-0.468291-3.140185-0.468476-3.177607-0.484179-3.215426-0.500065-3.215835-0.500254-3.254074-0.516336-3.292719-0.532605-3.293136-0.532798-3.332209-0.549266-3.371697-0.565925-3.372123-0.566123-3.412048-0.582986-3.452396-0.600044-3.452830-0.600246-3.493625-0.617512-3.534851-0.634979-3.535295-0.635185-3.576977-0.652864-3.619100-0.670747-3.619553-0.670958-3.662141-0.689058-3.705180-0.707367-3.705642-0.707582-3.749156-0.726113-3.793129-0.744857-3.793601-0.745077-3.838059-0.764047-3.882987-0.783236-3.883469-0.783461-3.928891-0.802881-3.974792-0.822523-3.975284-0.822753-4.021691-0.842632-4.068587-0.862739-4.069089-0.862973-4.116501-0.883321-4.164412-0.903902-4.164925-0.904141-4.213363-0.924969-4.262310-0.946034-4.262833-0.946278-4.312318-0.967595-4.362324-0.989155-4.362858-0.989405-4.413413-1.011222-4.464498-1.033287-4.465043-1.033543-4.516689-1.055871-4.568877-1.078452-4.569434-1.078713-4.622194-1.101563-4.675508-1.124672-4.676076-1.124939-4.729974-1.148322-4.784437-1.171970-4.785017-1.172243-4.840076-1.196171-4.895711-1.220369-4.896304-1.220647-4.952548-1.245132-5.009381-1.269892-5.009986-1.270177-5.067440-1.295230-5.125495-1.320565-5.126113-1.320855-5.184802-1.346489-5.244105-1.372411-5.244736-1.37270