Shilling

Bucket full of solvers for nth order non-linear ODEs all implemented in MATLAB.

List of Available Solvers

Fixed Step Solvers

Name	Description	Properties	Order	Stages	Registers	CFL	Reference
euler	Euler		1	1	1	1.0	Euler (1768)
midpoint	Midpoint		2	2	2		?
heun	Heun		2	2	2		?
rkssp22	2-stage, 2nd order TVD Runge-Kutta Shu-Osher	Strong stability preserving	2	2	1	1.0	Shu & Oscher (1988)
rk3	3th order Runge-Kutta		3	3	3		?
rkssp33	3-stage, 3rd order TVD Runge-Kutta Shu-Osher	Strong stability preserving	3	3	1	1.0	Shu & Oscher (1988)
rkssp53	5-stage, 3rd order SSP Runge-Kutta Spiteri-Ruuth	Strong stability preserving	3	5	2	2.65	Ruuth (2006)
rk4	Classic 4th order Runge-Kutta		4	4	4		Kutta (1901)
rks4	4th order Runge-Kutta Shanks		4	4	4		Shanks (1965)
rkr4	4th order Runge-Kutta Ralston		4	4	4		Ralston (1962)
rkls44	4-stage, 4th order low storage non-TVD Runge-Kutta Jiang-Shu	Low storage	4	4	2		Jiang and Shu (1988)
rkls54	5-stage, 4th order low storage Runge-Kutta Carpenter-Kennedy	Low storage	4	5	2	0.32	Carpenter & Kennedy (1994)
rkssp54	5-stage, 4th order SSP Runge-Kutta Spiteri-Ruuth	Strong stability preserving	4	5	4	1.51	Ruuth (2006)
rks5	5th order Runge-Kutta Shanks		5	5	5		Shanks (1965)
rk5	5th order Runge-Kutta		5	6	6		?
rkc5	5th order Runge-Kutta Cassity		5	6	6		Cassity (1966)
rkl5	5th order Runge-Kutta Lawson		5	6	6		Lawson (1966)
rklk5a	5th order Runge-Kutta Luther-Konen 1		5	6	6		Luther & Konen (1965)
rklk5b	5th order Runge-Kutta Luther-Konen 2		5	6	6		Luther & Konen (1965)
rkb6	6th order Runge-Kutta Butcher		6	7	7		Butcher (1963)
rk7	7th order Runge-Kutta Shanks		7	9	9		Shanks (1965)
rk8_10	10-stage, 8th order Runge-Kutta Shanks		8	10	10		Shanks (1965)
rkcv8	11-stage, 8th order Runge-Kutta Cooper-Verner		8	11	11		Cooper & Verner (1972)
rk8_12	12-stage, 8th order Runge-Kutta Shanks		8	12	12		Shanks (1965)
rkz10	10th order Runge-Kutta Zhang		10	16	16		Zhang (2019)
rko10	10th order Runge-Kutta Ono		10	17	17		Ono (2003)
rkh10	10th order Runge-Kutta Hairer		10	17	17		Hairer (1978)