Coupled odes involving mass matrix

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Sreeja Loho Choudhury 2020-7-27

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评论： Sreeja Loho Choudhury 2020-7-28

I am solving two coupled differential equations. The 1st ode is linear in the variable say x which is a function of time t. The first ode is simple like: dxdt=ax, a=constant.

The 2nd ode is coupled and linear in the variable y. y is a function of time t amd variable x. dydt involves the variable x and t both. Also the 2nd ode is of the form M(t,x)*dydt=F(t,y,x), where M(t,x) is the mass matrix which is a function of both time t and dependent variable x. How do I solve this two odes? And I don't want to invert the mass matrix present on the left hand side of the 2nd ode in order to solve dydt=M(t,x)^-1*F(t,y,x), as inverting the mass matrix produces the error message: Matrix is close to singular or badly scaled. So, I want to solve the 2nd ode by keeping the mass matrix as it is on the left hand side. Any input will be highly appreciated.

Thanks a lot.