Lotka-Volterra 2d with Lobatto VPRK Methods and Projections

VPRKLobattoIIIA(2)

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Simulation crashed after 0 of 10000 time steps: singular matrix.

LobattoIIIA(2) with standard projection

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Simulation crashed after 0 of 10000 time steps: singular matrix.

LobattoIIIA(2) with symmetric projection

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Simulation crashed after 0 of 10000 time steps: singular matrix.

LobattoIIIA(2) with symplectic projection

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Simulation crashed after 0 of 10000 time steps: singular matrix.

LobattoIIIA(2) with midpoint projection

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Simulation crashed after 0 of 10000 time steps: singular matrix.

LobattoIIIA(2) with internal stage projection

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Simulation crashed after 0 of 10000 time steps: MethodError.

VPRKLobattoIIIA(3)

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Simulation crashed after 0 of 10000 time steps: singular matrix.

LobattoIIIA(3) with standard projection

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Simulation crashed after 0 of 10000 time steps: singular matrix.

LobattoIIIA(3) with symmetric projection

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Simulation crashed after 3 of 10000 time steps: solver error – NaN detected in direction vector.

Lotka-Volterra 2d

LobattoIIIA(3) with symplectic projection

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Simulation crashed after 0 of 10000 time steps: singular matrix.

LobattoIIIA(3) with midpoint projection

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Simulation crashed after 3 of 10000 time steps: solver error – NaN detected in direction vector.

Lotka-Volterra 2d

LobattoIIIA(3) with internal stage projection

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Simulation crashed after 0 of 10000 time steps: MethodError.

VPRKLobattoIIIA(4)

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Simulation crashed after 0 of 10000 time steps: singular matrix.

LobattoIIIA(4) with standard projection

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Simulation crashed after 0 of 10000 time steps: singular matrix.

LobattoIIIA(4) with symmetric projection

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Simulation crashed after 2 of 10000 time steps: singular matrix.

Lotka-Volterra 2d

LobattoIIIA(4) with symplectic projection

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Simulation crashed after 0 of 10000 time steps: singular matrix.

LobattoIIIA(4) with midpoint projection

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Simulation crashed after 4 of 10000 time steps: solver error – NaN detected in direction vector.

Lotka-Volterra 2d

LobattoIIIA(4) with internal stage projection

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Simulation crashed after 0 of 10000 time steps: MethodError.

VPRKLobattoIIIB(2)

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Simulation crashed after 0 of 10000 time steps: singular matrix.

LobattoIIIB(2) with standard projection

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Simulation crashed after 0 of 10000 time steps: singular matrix.

LobattoIIIB(2) with symmetric projection

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Simulation crashed after 0 of 10000 time steps: singular matrix.

LobattoIIIB(2) with symplectic projection

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Simulation crashed after 0 of 10000 time steps: singular matrix.

LobattoIIIB(2) with midpoint projection

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Simulation crashed after 0 of 10000 time steps: singular matrix.

LobattoIIIB(2) with internal stage projection

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Simulation crashed after 0 of 10000 time steps: MethodError.

VPRKLobattoIIIB(3)

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Simulation crashed after 0 of 10000 time steps: singular matrix.

LobattoIIIB(3) with standard projection

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Simulation crashed after 0 of 10000 time steps: singular matrix.

LobattoIIIB(3) with symmetric projection

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Simulation crashed after 0 of 10000 time steps: singular matrix.

LobattoIIIB(3) with symplectic projection

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Simulation crashed after 0 of 10000 time steps: singular matrix.

LobattoIIIB(3) with midpoint projection

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Simulation crashed after 3 of 10000 time steps: solver error – NaN detected in direction vector.

Lotka-Volterra 2d

LobattoIIIB(3) with internal stage projection

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Simulation crashed after 0 of 10000 time steps: MethodError.

VPRKLobattoIIIB(4)

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Simulation crashed after 0 of 10000 time steps: singular matrix.

LobattoIIIB(4) with standard projection

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Simulation crashed after 0 of 10000 time steps: singular matrix.

LobattoIIIB(4) with symmetric projection

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Simulation crashed after 5 of 10000 time steps: solver error – NaN detected in direction vector.

Lotka-Volterra 2d

LobattoIIIB(4) with symplectic projection

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Simulation crashed after 0 of 10000 time steps: singular matrix.

LobattoIIIB(4) with midpoint projection

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Simulation crashed after 4 of 10000 time steps: solver error – NaN detected in direction vector.

Lotka-Volterra 2d

LobattoIIIB(4) with internal stage projection

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Simulation crashed after 0 of 10000 time steps: MethodError.

VPRKLobattoIIIC(2)

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Lotka-Volterra 2d

LobattoIIIC(2) with standard projection

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Lotka-Volterra 2d

LobattoIIIC(2) with symmetric projection

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Lotka-Volterra 2d

LobattoIIIC(2) with symplectic projection

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Lotka-Volterra 2d

LobattoIIIC(2) with midpoint projection

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Lotka-Volterra 2d

LobattoIIIC(2) with internal stage projection

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Simulation crashed after 0 of 10000 time steps: MethodError.

VPRKLobattoIIIC(3)

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Lotka-Volterra 2d

LobattoIIIC(3) with standard projection

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Lotka-Volterra 2d

LobattoIIIC(3) with symmetric projection

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Lotka-Volterra 2d

LobattoIIIC(3) with symplectic projection

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Lotka-Volterra 2d

LobattoIIIC(3) with midpoint projection

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Lotka-Volterra 2d

LobattoIIIC(3) with internal stage projection

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Simulation crashed after 0 of 10000 time steps: MethodError.

VPRKLobattoIIIC(4)

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Lotka-Volterra 2d

LobattoIIIC(4) with standard projection

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Lotka-Volterra 2d

LobattoIIIC(4) with symmetric projection

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Lotka-Volterra 2d

LobattoIIIC(4) with symplectic projection

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Lotka-Volterra 2d

LobattoIIIC(4) with midpoint projection

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Lotka-Volterra 2d

LobattoIIIC(4) with internal stage projection

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Simulation crashed after 0 of 10000 time steps: MethodError.

VPRKLobattoIIID(2)

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Lotka-Volterra 2d

LobattoIIID(2) with standard projection

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Lotka-Volterra 2d

LobattoIIID(2) with symmetric projection

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Lotka-Volterra 2d

LobattoIIID(2) with symplectic projection

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Lotka-Volterra 2d

LobattoIIID(2) with midpoint projection

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Lotka-Volterra 2d

LobattoIIID(2) with internal stage projection

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Simulation crashed after 0 of 10000 time steps: MethodError.

VPRKLobattoIIID(3)

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Lotka-Volterra 2d

LobattoIIID(3) with standard projection

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Lotka-Volterra 2d

LobattoIIID(3) with symmetric projection

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Lotka-Volterra 2d

LobattoIIID(3) with symplectic projection

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Lotka-Volterra 2d

LobattoIIID(3) with midpoint projection

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Lotka-Volterra 2d

LobattoIIID(3) with internal stage projection

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Simulation crashed after 0 of 10000 time steps: MethodError.

VPRKLobattoIIID(4)

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Lotka-Volterra 2d

LobattoIIID(4) with standard projection

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Lotka-Volterra 2d

LobattoIIID(4) with symmetric projection

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Lotka-Volterra 2d

LobattoIIID(4) with symplectic projection

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Lotka-Volterra 2d

LobattoIIID(4) with midpoint projection

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Lotka-Volterra 2d

LobattoIIID(4) with internal stage projection

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Simulation crashed after 0 of 10000 time steps: MethodError.

VPRKLobattoIIIE(2)

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Lotka-Volterra 2d

LobattoIIIE(2) with standard projection

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Lotka-Volterra 2d

LobattoIIIE(2) with symmetric projection

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Lotka-Volterra 2d

LobattoIIIE(2) with symplectic projection

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Lotka-Volterra 2d

LobattoIIIE(2) with midpoint projection

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Lotka-Volterra 2d

LobattoIIIE(2) with internal stage projection

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Simulation crashed after 0 of 10000 time steps: MethodError.

VPRKLobattoIIIE(3)

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Lotka-Volterra 2d

LobattoIIIE(3) with standard projection

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Lotka-Volterra 2d

LobattoIIIE(3) with symmetric projection

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Lotka-Volterra 2d

LobattoIIIE(3) with symplectic projection

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Lotka-Volterra 2d

LobattoIIIE(3) with midpoint projection

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Lotka-Volterra 2d

LobattoIIIE(3) with internal stage projection

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Simulation crashed after 0 of 10000 time steps: MethodError.

VPRKLobattoIIIE(4)

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Lotka-Volterra 2d

LobattoIIIE(4) with standard projection

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Lotka-Volterra 2d

LobattoIIIE(4) with symmetric projection

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Lotka-Volterra 2d

LobattoIIIE(4) with symplectic projection

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Lotka-Volterra 2d

LobattoIIIE(4) with midpoint projection

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Lotka-Volterra 2d

LobattoIIIE(4) with internal stage projection

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Simulation crashed after 0 of 10000 time steps: MethodError.

VPRKLobattoIIIF(2)

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Lotka-Volterra 2d

LobattoIIIF(2) with standard projection

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Lotka-Volterra 2d

LobattoIIIF(2) with symmetric projection

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Lotka-Volterra 2d

LobattoIIIF(2) with symplectic projection

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Lotka-Volterra 2d

LobattoIIIF(2) with midpoint projection

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Lotka-Volterra 2d

LobattoIIIF(2) with internal stage projection

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Simulation crashed after 0 of 10000 time steps: MethodError.

VPRKLobattoIIIF(3)

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Lotka-Volterra 2d

LobattoIIIF(3) with standard projection

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Lotka-Volterra 2d

LobattoIIIF(3) with symmetric projection

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Lotka-Volterra 2d

LobattoIIIF(3) with symplectic projection

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Lotka-Volterra 2d

LobattoIIIF(3) with midpoint projection

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Lotka-Volterra 2d

LobattoIIIF(3) with internal stage projection

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Simulation crashed after 0 of 10000 time steps: MethodError.

VPRKLobattoIIIF(4)

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Lotka-Volterra 2d

LobattoIIIF(4) with standard projection

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Lotka-Volterra 2d

LobattoIIIF(4) with symmetric projection

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Lotka-Volterra 2d

LobattoIIIF(4) with symplectic projection

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Lotka-Volterra 2d

LobattoIIIF(4) with midpoint projection

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Lotka-Volterra 2d

LobattoIIIF(4) with internal stage projection

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Simulation crashed after 0 of 10000 time steps: MethodError.

VPRKLobattoIIIG(2)

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Lotka-Volterra 2d

LobattoIIIG(2) with standard projection

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Lotka-Volterra 2d

LobattoIIIG(2) with symmetric projection

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Lotka-Volterra 2d

LobattoIIIG(2) with symplectic projection

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Lotka-Volterra 2d

LobattoIIIG(2) with midpoint projection

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Lotka-Volterra 2d

LobattoIIIG(2) with internal stage projection

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Simulation crashed after 0 of 10000 time steps: MethodError.

VPRKLobattoIIIG(3)

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Lotka-Volterra 2d

LobattoIIIG(3) with standard projection

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Lotka-Volterra 2d

LobattoIIIG(3) with symmetric projection

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Lotka-Volterra 2d

LobattoIIIG(3) with symplectic projection

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Lotka-Volterra 2d

LobattoIIIG(3) with midpoint projection

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Lotka-Volterra 2d

LobattoIIIG(3) with internal stage projection

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Simulation crashed after 0 of 10000 time steps: MethodError.

VPRKLobattoIIIG(4)

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Lotka-Volterra 2d

LobattoIIIG(4) with standard projection

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Lotka-Volterra 2d

LobattoIIIG(4) with symmetric projection

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Lotka-Volterra 2d

LobattoIIIG(4) with symplectic projection

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Lotka-Volterra 2d

LobattoIIIG(4) with midpoint projection

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Lotka-Volterra 2d

LobattoIIIG(4) with internal stage projection

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Simulation crashed after 0 of 10000 time steps: MethodError.