I need to discretize below equation with the error is no, Management Theories

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I need to discretize below equation with the error is no

I need to discretize below equation with the error is no more then O[delta(t2),delta(x2)].

I've discretized it using explicit method (I attached it) , but its errors are O[delta(t),delta(x2)]. So it might be worse than that I have to do.
Please help me to find the way to discretize the equation with the error in correct range. (I think the Taylor expension would be helpful but not sure.)

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Management Theories: I need to discretize below equation with the error is no

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