Solutions for optimal third order Runge-Kutta

  1. When m1 is set equal to zero,

    2. a21 = 0.6265382932,
    a31 = 0.6265382932,
    a32 = -0.5511124048,
    b1 = 0.6265382932,
    b2 = 0.8561435280,
    b3 = -0.4826818212,
    c2 = 0.6265382932,
    c3 = 0.0754258885,
    m1 = 0
    m2 = 1. + 2.55348259/m3,
    m3 = m3,

  2. When m1 is set equal to one,

    3. a21 = 0.7583779830,
    a31 = 1.516755966,
    a32 = -1.868016303,
    b1 = 0.5128366939,
    b2 = 0.6048107162,
    b3 = -0.1176474101,
    c2 = 0.7583779830,
    c3 = -0.3512603372,
    m1 = 1.
    m2 = 1. + 1.323771648/m3,
    m3 = m3,

    a21 = 2.325343935,
    a31 = 4.650687870,
    a32 = -0.6026659125,
    b1 = 0.6968727839,
    b2 = 0.4220554377,
    b3 = -0.1189282215,
    c2 = 2.325343935,
    c3 = 4.048021957,
    m1 = 1.
    m2 = 1. + 1.700314103/m3,
    m3 = m3,

  3. When m2 is set equal to one,

    4. a21 = 0.9245741122,
    a31 = 0.085748762,
    a32 = 0.2877129438,
    b1 = 0.085748762,
    b2 = 0.2877129438,
    b3 = 0.6265382937,
    c2 = 0.9245741122,
    c3 = 0.373461706,
    m1 = -0.9072559340,
    m2 = 1.
    m3 = m3,

  4. When m3 is set equal to zero,

    5. a21 = 0.9245741122,
    a31 = 0.085748762,
    a32 = 0.2877129438,
    b1 = 0.085748762,
    b2 = 0.2877129438,
    b3 = 0.6265382937,
    c2 = 0.9245741122,
    c3 = 0.373461706
    m1 = -0.9072559340,
    m2 = m2,
    m3 = 0,